Which Protestant Christian denominations accept the Deuterocanonical books?

I don't think there are any denominations outside of Catholicism accept deuterocanonical books. This is because of the testimony of Jewish Priest Josephus.

Jewish historian Josephus wrote about the canon used in the first century Israel. Against Apion, Book 1, Paragraph 8.

For we have not an innumerable multitude of books among us, disagreeing from and contradicting one another, [as the Greeks have,] but only twenty-two books, which contain the records of all the past times; which are justly believed to be divine; and of them five belong to Moses, which contain his laws and the traditions of the origin of mankind till his death. This interval of time was little short of three thousand years; but as to the time from the death of Moses till the reign of Artaxerxes king of Persia, who reigned after Xerxes, the prophets, who were after Moses, wrote down what was done in their times in thirteen books. The remaining four books contain hymns to God, and precepts for the conduct of human life. It is true, our history hath been written since Artaxerxes very particularly, but hath not been esteemed of the like authority with the former by our forefathers, because there hath not been an exact succession of prophets since that time; and how firmly we have given credit to these books of our own nation is evident by what we do; for during so many ages as have already passed, no one has been so bold as either to add any thing to them, to take any thing from them, or to make any change in them; but it is become natural to all Jews immediately, and from their very birth, to esteem these books to contain Divine doctrines, and to persist in them, and, if occasion be willingly to die for them.

Josephus mentions Ezra and Nehemiah in Antiquities of Jews Book XI, Chapter 5 and Esther (during the rule of Artaxerxes) in Antiquities of Jews Book XI, Chapter 6.

The canon is till the reign of Artaxerxes as mentioned by Josephus above in Against Apion Book 1, Paragraph 8.

Josephus mentions (above) why their history written since Artaxerxes are not part of his canon.

Josephus (Against Apion, Book 1, Paragraph 8) - "It is true, our history hath been written since Artaxerxes very particularly, but hath not been esteemed of the like authority with the former by our forefathers, because there hath not been an exact succession of prophets since that time;"

This is also agreed by 1 Maccabees. For Example, 1 Maccabees 4:46, 1 Maccabees 9:27, and 1 Maccabees 14:41 point out the lack of prophets during the Maccabean period.

1 Maccabees 4:46

And laid up the stones in the mountain of the temple in a convenient place, until there should come a prophet to shew what should be done with them.

1 Maccabees 9:27

So was there a great affliction in Israel, the like whereof was not since the time that a prophet was not seen among them.

1 Maccabees 14:41

Also that the Jews and priests were well pleased that Simon should be their governor and high priest for ever, until there should arise a faithful prophet;

When Josephus says 22 books, he is referring to 22 books in this order.

• Law of Moses (5 books)
  • Genesis
  • Exodus
  • Leviticus
  • Numbers
  • Deuteronomy
• Prophets (13 books)
  • Joshua
  • Judges
  • Ruth
  • Kings (1 Samuel - 2 Kings)
  • Chronicles (Both books)
  • Ezra-Nehemiah
  • Esther
  • Job
  • Isaiah
  • Jeremiah (includes Lamentations)
  • Ezekiel
  • Daniel
  • Twelve Prophets
• Hymns (4 books)
  • Psalms
  • Proverbs
  • Ecclesiastes
  • Song of Songs

All of the minor prophets are listed as "Twelve Prophets" in Sirach 49:10 and in the "Old Testament Canon" mentioned by Melito (Source - Ecclesiastical History 4.26.13–14).

In Septuagint, 1 Samuel - 2 Kings are listed as the part of Book of Kings (Source - http://ecmarsh.com/lxx/index.htm). Melito mentions 4 books (1 Samuel-2 Kings) as part of the book of Kings and 1 and 2 chronicles as part of the book of Chronicles. Ezra and Nehemiah are mentioned together in Josephus' Antiquities of Jews Book XI, Chapter 5.

Luke 24:44 also mentions that Jesus Christ came to fulfill the law of Moses, Prophets, and Psalms.

Luke 24:44 (NIV)

He said to them, “This is what I told you while I was still with you: Everything must be fulfilled that is written about me in the Law of Moses, the Prophets and the Psalms.

The 39 articles of religion in the back of the Book of Common Prayer, used by Anglicans and Episcopalians, says concerning these books (part of Article 6):

And the other Books (as Hierome saith) the Church doth read for example of life and instruction of manners; but yet doth it not apply them to establish any doctrine; such are these following:

It then lists all the books of the Apocrypha which were found in early editions of the King James Version. "Hierome" is, of course, Jerome who came up with the idea of calling these books the Apocrypha to begin with. So its not that they put these books "on equal inspirational footing as the rest of the Biblical canon" but that they are read at least. They aren't banned from the pulpit as they would be in a Baptist church. But according to the rule stated here, they can only be used as backup, not to create a new doctrine but only to backup what the Old and New Testaments already say anyway.

In the Daily Office lectionary of every pre-1979 Book of Common Prayer there are two lessons to be read at each sitting, one Old Testament and one New Testament lesson. Sometimes the Old Testament lesson comes from the Apocrypha.

The Revised Common Lectionary, a Sunday lectionary used by several Protestant denominations, also occasionally gives an optional reading from the Apocrypha in the Old Testament reading slot. It gives a choice, like for example in Year A on the 6th Sunday after Epiphany, it calls for: Deuteronomy 30:15-20 or Sirach 15:15-20

On the Revised Common Lectionary site's FAQ, under the question "What churches are current members of the Consultation on Common Texts?" they list the churches that are part of that consulation, which presumably means that they use the RCL. But that doesn't necessarily mean they read the optional readings from the Apocrypha.