I would say it depends on the cartridge it is chambered in.

Chris.

I''ve seem on the shiloh site that someone wrote that kirk, the owner said they would take anything a Ruger #1 would take....
Call shiloh and ask..!

Terry

It was somewhat of a sad story. These brothers had a respectable Sharps collection, a farm, and raised Buffalo back in the Eighties. So they chose to use this 45-120 to take one down old school. They sold me the gun because it just wasn't enough to bring the buffalo down. I was confused because a 45-120 should drop one like a rock. Their story was that they shot the critter and it just sat there in pain so they tried several more shots with no success so they got out their modern high power rifle to put it out of it's misery. Once I got it home and found that the cleaning rod kept getting stuck at the throat and fixed it, it was obvious why this 45-120 didn't meet expectations. Now it shoots like a dream (for a 45-120 in a Business rifle, Ouch  ).

Back on topic, as in many posts here, if you stick to calibers with 70 or less in there name for powder charge you should be OK with  plain based lead bullet loadings (no high speed stuff). 4198, 4895, 5744 (with some reservations), Reloader 7, etc. There are many available powders for these.

Pretty much with the quality of modern steels, the sharps action is pretty strong. I know a gunsmith that built one and I don't know who's casting he used, but he did a gove conversion to it in which the breach block tilts and will cam a round into the chamber. When I saw him last year he told me that he finally managed to blow his rifle up but would not say what the load was but I am sure that it was way above sane.
I would think that the Shiloh would be as strong or stronger than a Marlin and when your loads exceed those for a marlin your getting into the painful area. 
Or you could just stick with black and lead bullets. They will work surprisingly well.
Sam

Roscoe, since you didn't mention the caliber you might be interested in, look the calibers they make here ... 
(You need to Login or Register to view media files and links)

The most common is the 45-70 and as long as you reload with smokeless powder less than SAMMI 28,000 psi - you'd be in safe have.
As for the other calibers available, look up the SAMMI maximum psi's here ... (You need to Login or Register to view media files and links); The pressures are listed as Pressure Limits
(fps) (psi/100)(1)

Roscoe, 
FWIW, I've built, loaded and shot several of these rifles for years, (Shilo's, Winchester's, Remington's, Ballards, even Pedersoli's) started with black, convinced  myself early on that black was the only way, about ten or twelve years ago I experimented with duplex and smokeless both, I've settled on smokeless with results consistent and close to all the black I've burned.  What I really like about smokeless is the cleanup, the guns are the same, but the brass... cleaning the brass after a black load is a pita.   I load smokeless in .38 cal.,40's, 45's, 50's and getting ready in a .577. All I ever shoot is lead cast though, and I keep my velocities very similar to the loads in black powder.   My preferred powder is  5744, one of the secrets I have discovered  in loading this... Accurate claims this powder is not position sensitive, maybe not the smaller cases, but on the larger cases, I use a toilet paper filler, 1/4 to half sheet, and I use a card at the base of the bullet, this seems to improve consistency.  There are load specifications published by Accurate, start at minimums and don't chase max loadings just because they are there.  I discovered quite a while back, my guns and loads do extremely well, most of the issues are from the guy jerking the trigger, occasionally I find another place to place the blame, bullets, wind, sight, a particular gun, but mostly me.