I would have no doubt, at different times, Ol Jellystone backed several different rifles. In the primary time frame, the rifles of choice for those planning to foray into hostile territory were primarily Henry and 1866. Both of those choices had great magazine capacity.
Initially, the most common would have been the Henry. Available during and immediately after the War Between the States in fair numbers, the Henry would have been most common.
We also know, the manufacturers of the period were prone to make about anything anyone ordered. Many Stockiest of the day often placed orders for other than standard guns. The manufacturers were not necessarily keepers of perfectly pristine records. Many paper "trails" did not survive to the present day.
Gunsmith built Carbines would also have been quite .... rare. Cutting down a Henry pattern barrel is a lot more difficult than one would think. I know this 'cause I've done it. Elected not to do it twice.
Then we come to a whole new question. Posed Pictures purported particularly perfect. Photographer yells .. "Kelly needs a rifle" and able assistant hands our hero Jellystone a rifle and says "here .... use this one."
Let's face it folks. Those Halcyon days of Yesteryear were just that. Yesteryear. Not necessarily well documented, as when your actually living it, your not real concerned with what history will say.
Coffinmaker
(It's Saturday. The weather sucks. I'm real bored. I want SPRING!!)
PS: At least the rifle in the Pic was fully loaded.