Rossi 92 or Henry Big Boy for a lever
H&R/New England for a single shot.
I am unsure why 44 or 357 bolt guns exist but they will get the job done too.
My vote is for a lever action if only because it pairs well with a revolver. 44 rifles in general have spotty accuracy. .431 SAAMI bore diameters only exacerbate this.
After a many years long love affair with .44 (.429-.431 actual bore diameter) Which included revolvers, a 445 Super mag, 444 Marlin, and 44 rifles, I ditched it for the inconsistencies between handgun and rifle and the limited bullet selection for faster speed rounds like the 444 and the 444 Short and 44-06 I was working on wildcatting.
Threw it all in the bin in favor of the many and already extant 45 cal offerings such as 45 Colt, 450 Bushmaster, 454 Casull, and 460 S&W. Just worked out better for me.