Like the originals, the Pietta Smith Carbine is a .50 caliber gun. That caliber size indicates what the bore diameter is and because the rifling grooves are a larger diameter than the bore and because the gun is loaded from the breech, the bullet or ball must be larger than .50 caliber.
In my old 2005 Dixie Gun Works catalog they have an ad selling the Pietta Smith carbine. In it they say the bore diameter is .500". The rifling groove diameter is .514" and they recommended a .515 diameter conical bullet along with a 40 grain, 3Fg powder charge.
If Dixie sent some .520 diameter bullets or balls, they should work assuming you can load them into the rubber cartridge.
In another part of the same catalog, they offer two cartridge cases for the Smith. One is a brass case designed with a reduced powder capacity for target shooting. The other is a hard rubber case made out of modern rubber. (For those who don't know, the original Smith cartridges were made of natural rubber.
The cartridge case does not have a percussion cap or primer in it and the gun must be capped with a separate Musket size percussion cap. This cap is fired by a side hammer.
Because this gun uses a separate primer, it is now OK to talk about it on the MLF.)