So, if we actually look at the 1860 census, which lists the 100 largest cities in the U.S. (Atlanta, at # 99, is a good base line for the minimum size of the possible capitol) and look at all the cities that were in the Confederacy, we get:
6-New Orleans (large, but on the coast and Missisippi, so indefensible. also, not geographically central)
22-Charleston (on the coast, placing the capitol in SC just helps the fire eaters)
25-Richmond (OTL)
27-Mobile (on the coast, clearly defensible, but geographically very far south.)
38-Memphis (on the Missisippi, not defensible, too far west)
41-Savannah (on the coast, not too defensible)
50-Petersburg (if you control Petersburg, you control Richmond)
54-Nashville (close to Kentucky border, on river)
61-Norfolk (on the coast, again, why not go to Richmond if you have Norfolk)
77-Augusta(GA) (not on the coast, a bit small)
97-Columbus(GA) (geographically well placed but too small)
99-Atlanta (geographically well placed but too small)
This leaves Charleston, Mobile, Nashville, and Augusta as the other serious prospective options for capitol in my opinion, although they all have downsides compared to Richmond.