My thought is that Georgia would be one of the first ones to go, the governor of Georgia never seemed so keen about either side, and if the CSA won, would probably break off pretty quick. Not to mention, assuming that Sherman never came through, Atlanta is a decent capitol and Savannah is an excellent port, so Georgia would have the infastructure. Georgia would then go and colonize, since the soil in the actual state was getting worn out at the time.
There's a logistics problem here: Any newly independent CSA would be one of the smaller fish in the hemisphere, and any secession from the CSA would create a nation that was a small fish indeed. There'd be very few places to colonize that would be worth the effort that couldn't resist quite strongly. Especially when you consider that any major colonization effort requires military effort to pacify the natives. Any [plausible CSA independence scenario] requires a CSA that utilizes every bit of military force it has to the utmost. Sending a large chunk of that off to conquer [preferred colony here] is less that can be used to keep your own Unionists and enslaved down, while providing enough force to keep the North out.
Plus, any independent CSA is going to be a client of at least one if not two European powers. It's easy enough to see how any colonization effort by the CSA would be viewed as Monroe Doctrine issue, as the CSA acting as the catspaw of whichever paymaster got it independence.