Even after the Confederacy was desperately short of Soldiers, it was still enough of a "cornerstone" so that many refused to even consider recruiting slaves into the Army. It would have cut against the entire purpose of the Confederacy's existence.
"You cannot make soldiers of slaves, or slaves of soldiers. The day you make a soldier of them is the beginning of the end of the Revolution. And if slaves seem good soldiers, then our whole theory of slavery is wrong."
https://en.wikipedia.org/wiki/Howell_Cobb
They did in fact make soldiers out of slaves. For most of the Confederacy, the effort was near the end of the war, but Nathan Bedford Forest made 20 or so of his own slaves into cavalry with a promise of emancipation if they fought with him. They were quite effective. Prior to one battle, Forest signed all the manumission papers so that if he died, they would still have their freedom as he promised.
Only 1 deserted.