Technically speaking, the Confederate Constitution did not deny the states the right to abolish slavery. Yes, it says "No bill of attainder, ex post facto law, or law denying or impairing the right of property in negro slaves shall be passed" but that is in the context of the portion of Article I which deals with the powers of Congress, not of the states.
https://avalon.law.yale.edu/19th_century/csa_csa.asp When the Confederate Constitution wants to limit the powers of the states, it uses language specifically referring to the states: " No State shall enter into any treaty, alliance, or confederation; grant letters of marque and reprisal; coin money; make anything but gold and silver coin a tender in payment of debts; pass any bill of attainder, or ex post facto law, or law impairing the obligation of contracts; or grant any title of nobility." Note that this passage does not say anything about the "right of property in negro slaves."