I have a 45-120, it has been a long time since I have loaded any of my ammo, but I used Clean Shot back then, don't think that is available anymore, but any black powder will do. I used 500gr. Hornandy .458 Soft nose, they we're the most accurate. Basically, you load the black powder to the point of touching the base of the bullet, with my setup, it was with 100gr of Clean shot, you can try Pyrodex I used it as well. You can try the Pyrodex pellets, but you may need to add wadding in the case so there is no open space between bullet and powder. Good luck and have fun, I just hated cleaning mine. I have the David Pedersolli Quigley rifle.
Before you start loading the big old cases with black powder or their substitutes you need to do a bunch of research. Black powder can be gotten from Graf's, do a search you will find them. You can load with Pyrodex. What ever you use you need to have a compressed load, DO NOT LEAVE ANY AIR SPACE BETWEEN BULLET AND POWDER OR YOU WILL BLOW UP YOUR RIFLE. Basically you fill your case using a 30 inch or so long drop tube. A 30 inch length of copper tubing a little smaller in diameter than your case is what I use. Put a metal funnel on top. Always use metal not plastic when dealing with black powder or substitutes because of static electricity which will set it off. I made a way to clamp my drop tube to my loading bench. Trickle enough powder into the case through the drop tube until you reach the point that you can seat your bullet where you want it and still have enough room to place a disk made from waxed milk or orange juice etc. cartons or you can find vegetable fiber wads from Graf's and other places that are used as over powder wads and then be able to compress the powder down about 1/10 inch when you seat your bullet. Your powder weight will be between 90 and 110 grs depending on what bullet you use. Use magnum primers, Fed 215 works great. As for bullet molds Lyman 500 gr RN or their 520 Postel are good ones. You will need to use a pretty soft lead mix. Old fashion wheel weights are pretty good but are about as hard a mix as you will want to use. You will need a bullet lube made for lubing cast bullets used with black powder. SPG is great, Lyman makes one I think it is called BP Gold. I make my own by using a double bowler pan and melting bees wax and mixing it with Olive oil on a 50/50 by volume mix. This lube is to keep the fouling soft in your bore after you fire a shot. If the fouling is not soft so the next bullet can push it out of the way your accuracy will be terrible. Be ready with you pull the trigger because 90 to 110 gr of powder pushing 500 or so grs of lead will get your attention. Accurate powder makes a smokeless powder called XMP 5744 that you can also use in these big cases. Look up a Accurate loading manual it has data in it for the 45-120. By the way Sharps never made a case this big for their rifles. The 45-110 2 7/8" case was the largest case they made.
I would advise you to read the stamping on your barrel to see if it can handle smokeless powder, most Sharps rifles I have seen that are larger than 45-70 are black powder only. They don't recommend the smokeless powder due to pressure.