The only record I can find is from a year after the death of the man you're looking for.

A list of officer appointments in the 2nd (Slemons') Arkansas Cavalry, CSA, dated July 7, 1864, includes a Charles A. Christian, age 33, born in Alabama, who was appointed second lieutenant of Company I. This is one of the few surviving records of this regiment after its return to Arkansas.

Slemons' 2nd Arkansas Cavalry started with 8 companies, was reduced to 7 companies through consolidation; and was reinforced to 10 full companies in the summer of 1864, in preparation for the upcoming Missouri Campaign. No rosters of these new companies can be found, just a list of officer appointments. There is no earlier or later record of this Charles A. Christian.