Well.....can't say there's a lot of options here, but I can say that it wouldn't have been too hard to turn the Confederacy into such a state, in a scenario where it survives the Civil War; Southern religiousity of that time period, especially amongst good portions of the elite, often has been underestimated by many on here, based on my past observations at least.....and even IOTL, religion was not rarely connected to defenses of slavery in particular down there, just as religiousity was often tied to abolitionist sentiments up in the Northern states.
About the only major thing missing here, would be someone who could tie both fervent pro-slavery rhetoric and proto-Fundamentalist rhetoric together, though just who that might be could make for some very interesting debate.
That said, though, I don't think such a state, in this case, would emerge until after 1850, though the earlier the POD, the less challenging it would become.....