Darron,
A shipment of Enfield rifles was sent to Albert Sidney Johnston's army just before Shiloh - something like 3000 of them if memory serves.
This was not nearly enough to replace older arms of course. Many of the early battles like Mill Springs, Donelson and Shiloh wound find troops with flintlocks, shotguns, etc.
There were some modern arms in the Tennessee State Arsenal but not nearly enough.
Greg Biggs