.45-70 should do the trick. Back in the day, they used up to .50-110, but those were all black-power cartridges.
I’ve read where the 1886 Winchester (mine’s .40-82) was also chambered for the .50-110 at one time. It was called the ‘buffalo express’ or some such...
The 45-70 and its variants killed most of the buffalo. 45-70, 45-90,45-100, 45-110 and the 45-120 are all good. The 50s came out at the very end of the shooting, the early 1880s, and didn’t play that much of a role.
45-70 is the proper size for a buffalo gun, but I would get a Past shoulder pad, (Magnum) as the recoil can really damage (yes, damage) your shoulder. These guns are very near artillery.
My favorite buffalo rifle is my H&R Buffalo Classic. Based on a very early design (1860s) it looks like an English sporting rifle with a break open action.
It is a real screamer.......