Cortney- no wartime CS burials are located in the Memphis National Cemetary. It was not until the late 1970's that the rules changed to allow burial of confederate remains. Unless modern relitives requested it then, the only CS burials in a national cenmetary are those who also served in the post war army are unknown remains recovered in modern times.
Practice at the time for CS casualties was either mass burial on the battlefield(assuming the CS did not control the field after the battle) or burial in a local cemetary by members of the surrounding populace or the units involved.