How did Baptists in the southern US justify slavery as compatible with Christianity?

I have not been able to find evidence of a Baptist argument for slavery that differs from other pro-slavery denominations. Baptist minister Richard Furman (for whom Furman University was named) published a philosophical defense of slavery that alluded to biblical support but did not elaborate on it. The proof texts would have been well known to his readers.

The starting point for Christian justification of slavery is Genesis 9:24-27.

When Noah awoke from his wine and knew what his youngest son had done to him, he said, "Cursed be Canaan; lowest of slaves shall he be to his brothers." He also said, "Blessed by the Lord my God be Shem; and let Canaan be his slave. May God make space for Japheth, and let him live in the tents of Shem; and let Canaan be his slave."

From this a tradition arose that the curse gave Canaan black skin, and that he subsequently migrated to Africa. Although these ideas can't be found in the Bible, they dovetailed with a pro-slavery narrative. Author Anthony Pagden explains:

This reading of the Book of Genesis merged easily into a medieval iconographic tradition in which devils were always depicted as black. Later pseudo-scientific theories would be built around African skull shapes, dental structure, and body postures, in an attempt to find an unassailable argument--rooted in whatever the most persuasive contemporary idiom happened to be: law, theology, genealogy, or natural science -- why one part of the human race should live in perpetual indebtedness to another.

Exodus 21 contains rules and regulations for slave owners. A male Hebrew sold into slavery had to be released after six years, but females and children born into slavery could be held for life under certain conditions. A male slave could choose to remain a slave in order to stay with his family.

Deuteronomy 15:12-14 liberalizes some of the rules for Hebrew slaves, especially concerning who can be freed and what type of severance a freed slave should be given.

If a member of your community, whether a Hebrew man or a Hebrew woman, is sold to you and works for you six years, in the seventh year you shall set that person free. And when you send a male slave out from you a free person, you shall not send him out empty-handed. Provide liberally out of your flock, your threshing floor, and your wine press, thus giving to him some of the bounty with which the Lord your God has blessed you.

Rules for foreigners sold into slavery can be found in Leviticus 25:44-46. Regardless of age or gender, they could be held for life and could be inherited as property.

As for the male and female slaves whom you may have, it is from the nations around you that you may acquire male and female slaves. You may also acquire them from among the aliens residing with you, and from their families that are with you, who have been born in your land; and they may be your property. You may keep them as a possession for your children after you, for them to inherit as property. These you may treat as slaves, but as for your fellow Israelites, no one shall rule over the other with harshness.

That's probably the closest biblical match to slavery as it was practiced in the United States and Britain.

Slavery is taken for granted in many New Testament passages too. For example, in Ephesians 6:5-6 Paul¹ says:

Slaves, obey your earthly masters with fear and trembling, in singleness of heart, as you obey Christ; not only while being watched, and in order to please them, but as slaves of Christ, doing the will of God from the heart.

This is followed a few verses later (Ephesians 6:9) with:

And, masters, do the same to them. Stop threatening them, for you know that both of you have the same Master in heaven, and with him there is no partiality.

The phrase "both of you have the same Master" can be--and has been--interpreted to mean Paul is giving instructions to Christian masters of Christian slaves.

Similar instructions appear in Colossians 3:22-4:1.

Titus 2:9-10 states:

Tell slaves to be submissive to their masters and to give satisfaction in every respect; they are not to talk back, not to pilfer, but to show complete and perfect fidelity, so that in everything they may be an ornament to the doctrine of God our Savior.

Finally, 1 Peter 2:18-21 commands slaves to accept whatever harsh treatment their masters deal out.

Slaves, accept the authority of your masters with all deference, not only those who are kind and gentle but also those who are harsh. For it is a credit to you if, being aware of God, you endure pain while suffering unjustly. If you endure when you are beaten for doing wrong, what credit is that? But if you endure when you do right and suffer for it, you have God's approval. For to this you have been called, because Christ also suffered for you, leaving you an example, so that you should follow in his steps.

These last two passages have no corresponding instructions for slaveholders.

In conclusion, the Bible contains many passages--in both the Old and New Testaments--that have been used to justify slavery.

¹ Many modern scholars do not believe Paul wrote Titus, Ephesians, or Colossians, in part because they doubt the man who had said, "There is neither Jew nor Gentile, neither slave nor free, nor is there male and female, for you are all one in Christ Jesus," (Galatians 3:28), and who urged Philemon to free Onesimus and accept him as a brother (Philemon 1:15-16), would have been so accommodating to slavery.