Great question. A book I highly recommend is Mark Noll's The Civil War as a Theological Crisis, which has answers to a lot of the questions I think you'll have. Luke Harlow's The World the Civil War Made also contains a great chapter on this topic.

You could also go for Upon the Altar of the Nation: A Moral History of the Civil War or God's Almost Chosen People: A Religious History of the American Civil War.

It's important to note that not all Christians believed slavery was a moral thing. In fact, slavery was the very topic that led to the American Methodist, Baptist and Presbyterian churches to fission during the Civil War.

It was very literally a battle between Biblical literalism and those who believed the spirit rather than the absolute letter of the book should win out. Slaveholders favored the literal approach. As Presbyterian theologian Robert Lewis Dabney explained:

"we must go before the nation with the Bible as the text, and 'Thus saith the Lord' as the answer. ... we know that on the Bible argument the abolition party will be driven to unveil their true infidel tendencies. The Bible being bound to stand on our side, they have to come out and array themselves against the Bible. And then the whole body of sincere believers at the North will have to array themselves, though unwillingly, on our side. They will prefer the Bible to abolitionism."

To directly answer the question, look to the words of Presbyterian minister James Henley Thornwell, who in November 1860 declared to his South Carolina congregation: "That the relation betwixt the slave and his master is not inconsistent with the word of God, we have long since settled. ... We cherish the institution not from avarice, but from principle."

As Rable writes in God's Almost Chosen Peoples, "Sola scriptura both set and limited the terms for discussing slavery and gave apologists for the institution great advantages. The patriarchs of the Old Testament had owned slaves, Mosaic Law had upheld slavery, Jesus had not condemned slavery, and the apostles had advised slaves to obey their masters ─ these points both summed up and closed the case for many Southerners and no small number of Northerners."

To me, the Northern arguments are much more fascinating. Men like Henry Ward Beecher, a Congregational minister who was the North's most famous preacher, supported abolition, but they were going against what the Bible literally said. They had to come up with the much more creative arguments to support the abolitionist view.

I like the line quoted by Noll from Tayler Lewis, a professor of Greek and Oriental Studies (that was the term in use at the time, so pardon its use here) at New York University and Union College: "there is ... something in the more interior spirit of those [biblical] texts that [Van Dyke] docs not see; he docs not take the apostles' standpoint; he does not rake into view the vastly changed condition of the world; he does not seem to consider that whilst truth is fixed ... its application to distant ages, and differing circumstances, is so varying continually that a wrong direction given to the more truthful exegesis may convert it into the more malignant falsehood." (emphasis mine)

It's also important to note that the religious divide over slavery did not divide simply into North/South or even Christian/non-Christian. One of the most fascinating people examined by Noll is the rabbi Morris Raphall, who to the Jewish Synagogue of New York declared that African slavery was deemed by God to be appropriate in Genesis 9. While he said there were problems with slavery as it was practiced in the United States, Raphall was a firm believer in the institution.