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)
- Prophets (13 books)
- Kings (1 Samuel - 2 Kings)
- Chronicles (Both books)
- Jeremiah (includes Lamentations)
- Twelve Prophets
- Hymns (4 books)
- 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
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.