I was watching Pawn Stars and guy brought in a 1750's side by side muzzle loading coach gun. It had maybe a 12 inch barrel and a full stock. (Also a spring loaded bayonet) Do athe NFA rules apply to black powder guns?
No, I do not believe the NFA rules apply to a muzzle loading BP shotgun. Same as a muzzle loading cannon is not a DD. It generally has to be a "firearm" before anything NFA applies, but with non-firearm (i.e antique) self-contained metallic cartridge firing guns, things can be different. Machineguns are an exception (always NFA to my knowledge), while other self-contained metallic cartridge firing guns (SBRs and DDs) are decided case-by-case. Needless to say, it gets real fuzzy real quick when dealing with self-contained metallic cartridge guns from the 1880s-1890s (they may or may not be an SBR or DD). Also, please note that the "self-contained" distinction is important for things like the Billinghurst-Requa volley gun, which could be considered a machinegun, except for the fact that the cartridges use an external musket cap for ignition (the cartridges have a tiny flash hole in the back).