Most of the U.S. military rifles and carbines were sighted to hit a man on horseback, or the horse itself at about 325 yards. The result is that they will hit 12-15 inches high at 100 yds. The cartridge conversion Sharps carbines have a front sight blade that is pinned to the base, so the front sight can be replaced with a taller blade to bring the point of impact down.
While the M1869 Conversions (using 1858 and 1863 percussion carbines) are a relatively strong action, keep in mind that they are 164 years old. Even one with a nearly pristine barrel (and they seldom are) could have intergranular corrosion somewhere in the metal. I had one that had some historical provinance that I used to shoot, but have retired it out of respect to its history.
My suggestion would be to buy one of the modern reproductions in .45-70 or, if available, .50-70.
Safe shooting! Happy, Healthy and Safe New Year!