The Confederate constitution says "A well-regulated militia being necessary to the security of a free State, the right of the people to keep and bear arms shall not be infringed." There's debate about what the Second Amendment meant to the Founding Fathers, whether it protects an individual right to guns, what the "well-regulated militia" part means... Is there any consensus on what it meant to the Confederates?
There isn't much of an answer to that question, as far as I'm aware. The Judicial Branch (ie Supreme Court) of the Confederate States of America was never formed, meaning there is no rulings we can read to understand how their Second Amendment might have been applied.
However, we can make a few reasonable guesses. Prior to Incorporation of the Bill of Rights in the 20th Century, not to mention the passing of the 14th Amendment that made it possible following the Civil War, the Bill of Rights was understood to really just apply to the Federal Government. Given the strong states' rights views espoused by the Confederates, not to mention added into their Constitution, we would have every reason to believe that they would have read the 2nd Amendment to apply to the Confederate government, but not to the states, who would be able to put stronger policies in place as they saw fit.
This old answer I wrote up deals a good bit with pre-Incorporation understanding of the 2nd Amendment, and should help you out here I would hope.
when would it have come up? besides no guns for slaves the classic early 2nd amendment interp that at least part of it was to guarentee militia access to guns and since all guns were being used to fight a war for independence it would never have come up.
also given that it was copied verbatium i would argue there wasn't a real difference between confederate and older american thought on the issue