How do Christian apologists defend the credibility of the miracles reported in the gospel accounts?

The other responses touch on several aspects. The defense is a chain of reasoning.

1. Manuscript transmition fidelity. Many arguments speak of the large number of ancient copies of the Bible or citations and the closeness in time to the originals compared to other ancient documents, their general agreement, the fact that only 1% of all textual variants are both viable (in several MSS) and consequential, and they do not call into question any major doctrines.

2. Archeology. Many details of ancient culture, architecture, cities, people'e names, etc. have been verified by archaeology.

3. Varied viewpoints. The gospels differ in viewpoint, details shown or withheld, and stories told. Most differences have reasonable explantions that can be used to harmonize the accounts. If they were carbon copies, that would smack of collusion between a group trying to pull off a fraud.

4. Execution of the Apostles and others. Few people are willing to die for something they know to be a lie.

5. Spiritual benefits. The placebo effect notwithstanding, Jesus promised that the truth would set people free. Lying miracles should not cause true miracles to happen to people over the millennia. Years ago, I had gone deaf in my left ear, and after a month of treatment the doctor told me I would probably never recover my hearing. At the ear doctor's office, I opened my Bible and read this (part of the account of Moses seeing the burning bush):

11 The Lord said to him, “Who gave human beings their mouths? Who makes them deaf or mute? Who gives them sight or makes them blind? Is it not I, the Lord? 12 Now go; I will help you speak and will teach you what to say.” (Exodus 4:11-12)

Upon reading those words, I felt comforted that God was with me and knew what was going on. I experienced great peace. Two days later, my hearing returned.

6. Prophecy. To prove one miracle, look for another. The Bible is filled with prophecies that later came true. If a passage where Jesus performed a miracle is also a prophetic parable about the future, and the predicted events come to pass, you know that the original words about the miracle have not been tampered with, otherwise the prophecy would have been destroyed as well. I have found dozens of prophecies in Matthew alone and am preparing a book on them.

To complement what the other answers have already said, I think it is worth to cite Craig S. Keener's magisterial work Miracles: The Credibility of the New Testament Accounts. The preface says:

Most modern prejudice against biblical miracle reports depends on David Hume's argument that uniform human experience precluded miracles. Yet current research shows that human experience is far from uniform. In fact, hundreds of millions of people today claim to have experienced miracles. New Testament scholar Craig Keener argues that it is time to rethink Hume's argument in light of the contemporary evidence available to us. This wide-ranging and meticulously researched two-volume study presents the most thorough current defense of the credibility of the miracle reports in the Gospels and Acts. Drawing on claims from a range of global cultures and taking a multidisciplinary approach to the topic, Keener suggests that many miracle accounts throughout history and from contemporary times are best explained as genuine divine acts, lending credence to the biblical miracle reports.

An informative review of the book written by Michael J. Kruger is available here: https://www.thegospelcoalition.org/themelios/review/miracles-the-credibility-of-the-new-testament-accounts/:

Every once in a while a book comes along that is long overdue within the academic community. Craig Keener's Miracles is just such a book. Ever since the rise of the Enlightenment, academic circles have been inculcated with a naturalistic, anti-supernatural bias that pervades almost every discipline, from sociology to anthropology to psychology. And the discipline of biblical studies is no exception to that rule. When it comes to the miracles contained in the NT accounts, scholars have been chronically skeptical of their veracity and credibility. Keener's work is designed to challenge that bias. His intent is not to prove the truth of the NT miracles, nor of modern ones, but simply to show that the accepted predisposition against the possibility of miracles is intellectually indefensible. Of course, Keener's book is not the first to challenge the modern predisposition against miracles. But his book is unique in that it is up-to-date on the latest scholarship, vast in its detail and documentation (over 1,000 pages!), pays particular attention to ancient historiography, and offers an impressive catalog of modern (and ancient) miracle testimonies.

Keener offers two main arguments in the book, a historical one and a philosophical one. (1) The historical argument is that the miracle reports in the Gospels and Acts are based on eyewitness testimony (not legendary accretions or the invention of the later church). Put simply, we have solid historical evidence that the earliest followers of Jesus (and the apostles) thought they were witnessing miracles. Such ancient testimony to miracles, argues Keener, is analogous to what happens today when we receive reports that people have witnessed miracles. (2) The philosophical argument is that supernatural explanations for these miracle claims should not be ruled out from the very start. Instead, many of these miracle claims are best explained by supernatural causation, and the modern historian should at least be open to that possibility.

In order to address the historical question, Keener devotes the first three chapters to an in-depth investigation of the miracle accounts in the Gospels. Chapter one examines the Gospel accounts directly and argues that the miracle accounts of Jesus are central to the narrative of Jesus' life and are present in the earliest layers of the tradition (and thus unlikely to be later, mythical additions). Chapters two and three compare and contrast the miracle accounts in the Gospels with the miracle accounts in other Greco-Roman and Jewish literature. Keener demonstrates that although there are broad similarities between these extra-biblical miracle accounts and those of the Gospels, there are also significant differences. Thus, we have no reason to think that the miracle stories in the Gospels are due to the influence of pagan stories of magic and divination. Instead, the influence is often the other way around. Given Keener's extensive background in historical Jesus studies, his analysis in these chapters is first-rate: thorough, insightful, and attentive to the complex historical details.

Chapters 4-6 address the philosophical question of whether modern historians ought to reject miraculous explanations a priori. After a fascinating survey of the history of anti-supernaturalism in chapter four, Keener devotes the next two chapters to the most significant proponent of anti-supernaturalism: David Hume. Although modern philosophers have largely debunked Hume's arguments, some biblical scholars still appeal to these arguments to support their anti-supernatural bias. The problem, as Keener so deftly points out, is that Hume's argument is fallaciously circular: “[Hume] argues, based on 'experience,' that miracles do not happen, yet dismisses credible eyewitness testimony for miracles (i.e., others' experience) on his assumption that miracles do not happen” (p. 109, emphasis his). Put differently, Hume's argument is based on the “uniformity of human experience against miracles” (p. 112); a uniformity that he can establish only if he rejects, a priori, all eyewitness claims to miracles. Thus, he assumes what he is trying to prove.

One of the reasons Hume was able to appeal to the supposed “uniformity of human experience against miracles” is because of the “lack of many comparable modern claims” (p. 209) in his own day. In other words, Hume and his contemporaries did not have access to the abundant miracle claims in the world around them. Keener seeks to remedy this problem by devoting a significant portion of his book, chapters 7-12, to cataloging the variety of miracle reports available in our modern time. This is a most fascinating section of the book and stunningly rich in detail and documentation. Keener offers accounts from all over the world, but focuses mainly on the “majority world,” including Asia, Africa, Latin America, and the Caribbean. Not only does this survey effectively refute Hume's appeal to the uniformity of human experience against miracles, but it also effectively challenges traditional Western assumptions about religion in the developing world. Anti-supernaturalists will often dismiss miracle claims from these parts of the world due to the fact that they view the inhabitants as primitive, uneducated, and, to some extent, gullible. But Keener points out that such an approach is blatantly “ethnocentric” and “derogatory” (p. 222). Thus, the academic elite in America and Europe find themselves in an ironic dilemma. While they are often quick to critique others for being ethnocentric, they find themselves guilty of these very charges when they reject the miracle claims of the non-Western world on the basis of its so-called “primitive” culture.

Of course, Keener is well aware that not all of these miracle claims around the world are valid instances of miracles; some have other (and better) explanations. Thus, chapters 13-14 discuss other possible explanations for such claims, such as fraud, genuine anomalies, psychosomatic cures, the placebo effect, and the power of suggestion. While acknowledging that sometimes these factors can account for eyewitness miracle claims, it is not intellectually credible to think that such things can explain all miracle claims. Indeed, chapter 14 demonstrates that there have been formal investigations into miracles claims that have sought only to find alternative explanations, rather than being genuinely open to the possibility of divine intervention. These investigations, he argues, are overtly prejudiced against religion and use unreasonable standards for what can count as a “credible” miracle claim-standards that would not be sustained in other areas of life (e.g., a court of law).

In the end, Keener has written an impressive and well-argued work on a very important subject. Not only has he reiterated the long-standing critiques against Hume in a fresh way, but he has broken new ground by exploring modern miracle claims with unprecedented documentation. Any future discussions of miracles in the NT or in the modern day will surely have to reckon with the arguments of this book.

My general way of defending miracles goes like this:

1. God's existence and the existence of the spiritual world would raise the prior probability of miracle claims.
2. God exists.
3. If God exists, then things not made of material exist, and thus the supernatural world exists.
4. Thus, miracles have a higher probability.

This is a simple argument, but it works. Now obviously the question is still to be asked, do miracles only happen to the believers of one religion? This is slightly more complicated.

My major point is that demons could perform acts that deny the natural worlds order and laws. Thus we could say that demons perform miracles that are seen in other religions. Otherwise, we could say God has sufficient reasons to grant miracle requests to other religions.

Man prefers to believe what he prefers to be true.
_{Francis Bacon}

So, the bottom line regarding any "truth", even Francis Bacon's own observation, is a matter of what a reader/hearer prefers.

The Law given to Moses establishes the criterion for the "truth" of any matter:

¹⁵One witness shall not rise up against a man for any iniquity, or for any sin, in any sin that he sinneth: at the mouth of two witnesses, or at the mouth of three witnesses, shall the matter be established.
¹⁶If a false witness rise up against any man to testify against him that which is wrong; ¹⁷Then both the men, between whom the controversy is, shall stand before the LORD, before the priests and the judges, which shall be in those days; ¹⁸And the judges shall make diligent inquisition: and, behold, if the witness be a false witness, and hath testified falsely against his brother;
¹⁹Then shall ye do unto him, as he had thought to have done unto his brother: so shalt thou put the evil away from among you. ²⁰And those which remain shall hear, and fear, and shall henceforth commit no more any such evil among you.
²¹And thine eye shall not pity; but life shall go for life, eye for eye, tooth for tooth, hand for hand, foot for foot.
_{Deuteronomy 19:15-21 (KJV)}

The Gospel authors would have understood this principle, and to manufacture/exaggerate testimony would be in flagrant opposition to their faith in God. Of course, if one prefers to believe they did so, the question would still need to be answered, "Why do I prefer to dismiss what the Gospel authors have written as manufactured/exaggerated?"

However, in support of Jesus' works as authentic, John records this:

³¹Then the Jews took up stones again to stone him.
³²Jesus answered them, Many good works have I showed you from my Father; for which of those works do ye stone me?
³³The Jews answered him, saying, For a good work we stone thee not; but for blasphemy; and because that thou, being a man, makest thyself God.
_{John 10:31-33 (KJV)}

The Jews didn't contest Jesus' "good works" because they, themselves, witnessed many of them. For example:

• the man in the synagogue at Capernaum, from whom he drove out an evil spirit -- Mark 1:21-27.
• the man healed, sick of the palsy, to whom Jesus said, "Thy sins are forgiven" -- Matthew 8:1-7.
• etc.

The OP appears to prefer that Jesus' miracles were fictitious, or at best, exaggerated, but what evidence has been offered in support of that claim? The onus is not on those who accept as authentic the testimony provided by the Gospels, because their record of TESTIMONY EXISTS for all to consider. Rather, the onus is on those who challenge the authenticity of Jesus' miracles to provide evidence for why they prefer to do so. What TESTIMONY EXISTS that refutes it? How much weight should be given to a claim that a witness, or recorder of witness, has lied/exaggerated if NO TESTIMONY EXISTS that supports the claim?

If one seriously considers,...
A major concern with the rationality of belief in miracles is with whether we can be justified in believing that a miracle has occurred on the basis of testimony.,
... why do they not consider,...
A major concern with the rationality of unbelief in miracles is with whether we can justify not believing that a miracle has occurred on the basis of NO testimony.
... to be a weightier consideration.

The miracles don't need to be defended, the testimony recorded in the Gospels does a sufficient job for anyone who has no reason to think the Gospel authors lied/exaggerated their records.

For those who prefer to believe the accounts are fictitious/exaggerated, no number of witnesses will suffice to dissuade them from what they prefer. Only the work of the Holy Spirit within their hearts will have any possibility of conviction that they are mistaken.

Jesus said:

⁷Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you. ⁸And when he is come, he will reprove the world of sin, and of righteousness, and of judgment:
⁹Of sin, because they believe not on me; ¹⁰Of righteousness, because I go to my Father, and ye see me no more; ¹¹Of judgment, because the prince of this world is judged.
_{John 16:7-11 (KJV)}

The only sin that matters in regard eternal destiny is belief in Jesus. That is so, because rejecting the integrity of the one who has authority to determine it, makes only one destiny possible.

To deny the miracles of Jesus is clear evidence that one doesn't believe in Jesus. Again, the question needs to be asked, "Who is testifying that the Gospel writers lied/exaggerated concerning Jesus' miraculous works?" Jesus' enemies didn't dispute them at the time, so doubting them now, centuries and millennia after, should surely spark concern that one's thinking is not right.