1860 to 1875 is a pretty long period. not neccisarily in years, but evolution of weapons.
If you are choosing a cartridge that didn't exist (.357, .38 spec., 44 mag), then you may well be out of luck after a time. Let's remember that even though the classic Colt Peacemaker was introduced in 1873 it probably wasn't in very wide spread use until several years after that. and then you must consider a caliber.
I'd love to say Schofield, but again ammo could be an issue.
I'd also like to say a "cartridge conversion" 1860, but I don't know any specifics of reliability, etc.
Wonder if I could get Ruger to make me a GP100 with a 4" barrel in .44-40?