The South didn't adopt modern guns because of logistical consideration.
No one gave it a thought in 1861. Almost everybody on both sides accepted that the war would be a short, relatively quick war and the boys would be home in time for Christmas. Old Fuss and Feathers Winfield Scott knew otherwise but who wanted to hear about his drawn out two year Anaconda Plan? Before Manassas shattered the illusion of a quick war, the South was scrambling for any guns they could get. Besides the arms that were seized from los federales, the South was converting hunting guns to military service. McDowell and later Little Mac both (inadvertantly) did their share in helping supply the South.
Again, the problem remains that until the gas seal problem (resolved with the metallic cartridge case) and fouling issue were resolved (with nitro-cellulose propellants), automatic weapons were not feasible.
Vigilantibus et non dormientibus jura subveniunt. Molon Labe!