I was reading a facfic where Clark from one time frame meets Clark from another, and Lois refers to the one from the younger time-frame as CJ.
There was also a fan fic where CJ was a Clark from a different dimension (where solar-radiation is lower, so he does not have super powers, and he is an assistant DA in a Metropolis plagued by courts corrupted by Luthor.)
It seems to me more often Clark and Lois' oldest son gets named Jonathan than CJ, but naming him Clark Jerome Kent Jr. and calling him CJ works.
