East Tennessee, without a doubt. Tennessee had questionable loyalties to the Confederacy at first, since most viewed the idea as illegitimate, and Tennessee turned down secession at first. Lincoln's call for soldiers helped push Tennessee into the Confederate camp, but even that vote was very contested, and the vote in the state was very divided, and pushed for because of the governor Isham G. Harris. East Tennessee, with very little reliance on slavery, strong unionism, and very different economy than the rest of the state, very well could have split off, and they actually tried to gain West Virginia-esque recognition with the East Tennessee Convention.
I think Tennessee split between East Tennessee, Middle Tennessee, and West Tennessee is a possibility considering the Civil War. Only in West Tennessee was there overwhelming support of the CSA--Middle Tennessee voted for it too, but I wonder if it could be swayed the other way, since it was far closer than West Tennessee. There's certainly lots of land which is totally unsuitable for the chattel slavery which the CSA stood for.