If, by "modern loads" you mean the high pressure, high velocity stuff the specialty shops like Buffalo Bore and Garrett sell, the answer is no, even NO!. The Trapdoor Springfield reproductions are made out of better steel, but that does not make up for a black powder design. The only thing the reproduction will do that an original won't is shoot standard smokeless loads with jacketed bullets with decent accuracy and low wear and tear.
You can get reproductions of all four models of Sharps cartridge rifles, Winchester Single Shot, Remington Rolling Block, Remington Hepburn, Ballard, Stevens 44 1/2, and Peabody that I can think of offhand.
Reproduction repeaters include about all Winchesters. There were several attempts at making Colt Lightning pumps but I don't think anybody got the bugs out. There is a repro Burgess lever action. Marlins are still in production to what is pretty much the 1893 design and look "right" if you get a blue gun with walnut stock.
If you want to look for and pay for a sound original antique, the sky is the limit, both on guns available and price to be paid.
The field is huge and I don't feel qualified to spend your money for you. Get some books, go to some CAS and BPCR shoots to see period guns in action, and make a study of it.
Me?
Winchester Single Shot "Highwall" .38-55
Miroku/Browning modern knockoff of same .40-65.
Winchester 1892 .44-40.