There a a couple different loads to look for, and Sharps was a bit different than Remington. 

I believe it was Remington that had a 50 Navy carbine load that was around 50-55 grains. Used the standard bullet, but The case might have been shortened. Only read about it, never seen one.

For Sharps the original percussion rifle load was insert the ball, drop 55 grains into the chamber.

For my Sharps cavalry carbine I have two loads for 1.5 Swiss and Lyman 515141 425 grain bullet.

If I want the bullet to start engraving into the rifling and slightly compress the powder, I load 65 grains by weight.

Roughly 50 grains of powder allows for slight compression and the bullet is seated with the case mouth just above the top lube groove and a slight crimp.

With a rifle that weighs in just under 8#, the 15 grains is noticeable.

Accuracy is about the same. With original the rear sight, I can see the target and either the front or rear sight. It’s just fun to shoot.

Did you do a chamber cast? Will it chamber a 50-70 cart or the shorter 50-45? -

Have you slugged the bore to find groove and bore size? .50-70s vary a lot. Size your bullets to groove size or .001" over. My NY state rifle runs .510" which is unusually small. 

Since I have 3 carbines in 50-70, I have been trying about 62 grains GOEX FFg and the Lyman 515139 (350 grain) bullet.   I had hoped to do more experimenting this year but other things kept getting in the way.  I did try that in my 50-70 Peabody and it shot reasonably well.   I use that same bullet with 40 to 45 grains of FFFg in several other carbines  (Maynard, Spencer, and 56-50 Peabody).  Those loads are much easier on the shoulder.   The NY Carbine is chambered for the 50-70.   I don't think anything but those early USN carbines used the 50-45 (shorter) carbine round.

George