The State of Texas issued Sharps carbines in 50-70 to the Rangers. They were conversions from the linen cartridge. When the Winchester 73 came out, The Rangers ditched the Sharps in favor of the Winchester and had to buy them out of their own pocket. Some Rangers continued to use the state issued rifle for some years later. Most did not.
So, a 50-70 Sharps carbine was correct for the movie.