Granted most "Enfields" in the CSA were London Armory Company three band rifles...... But I believe that in the South P56 two band rifles were not "uncommon"
I do not have the numbers in front of me but I suspect they were at least as common as 1841 Rifles.
The LAC P53s were relatively common because the CSA contracted for the total output of that company before the Union was able to and LAC was an approved substitute for UK military and such and was capable of large scale production with full interchangeable parts.
Because of the Crimean War and the forming of Volunteer Rifle Corps in Great Britain a number of firms had set about to make both three band and two band rifles and even some carbines. The Government there was concerned about taking care of all these different make of rifles should these units be called up and had just announced they would be the source of such rifles from either the Enfield Arsenal or LAC.
This left a bunch of folks with rifles no one in Britain wanted and the Government failed to obtain an exclusive contract from LAC.
Many of the Volunteer rifles were assemblages of parts from various contractors amassed and assembled by the "Maker" and some were what might be called standard only out of politeness. On the other hand as I meantioned William Greener made excellent two band rifles with atleast two different types of rifling to his high standards.... and cost.
In the CSA Enfields of all types were rated as those that had no interchangeable parts, to those that had interchangeable with in a lot of rifles or with in an issued unit, and those like the LAC guns that were fully interchangeable.
Keep in mind that early in the war, at least in the South, it was pretty much "dance with the girl you brought" as men assembled in county seats with whatever miss match of guns they had. This made ammunition supply "catch as catch can" and weapons repair anyone's guess.
A large number of Militia on both sides would fight in 1861 with smooth bore muskets with only a front sight, or bayonet mount really, and many of those would be converted flint lock and some not converted. Flintlock smooth bores were used in combat against Union troops as late as 1865 at the Battle of Natural Bridge Florida......and held the line.
-kBob