The 1874 Sharps is the most common, Made in America Shiloh and C. Sharps preferred, Pedersoli the best of the imports.
Even though they haven't been made in 10+ years, the Browning BPCR on a modified Highwall action is very popular. There have been a few the same with Winchester markings.
Otherwise, real Winchesters and new or old Rolling Blocks are pretty common; along with a few CPA Stevens and Ballards. The C. Sharps 1875 is a good deal, less expensive than their 1874s but just as accurate even though not as pretty. There are a few Remington Hepburns around and I have seen one ever Miller Model F on the Farrow design. There is a Peabody reproduction but I have not seen one in use.
An NRA Black Powder Silhouette or Target Rifle must be a single shot.
The Silhouette rifle must have an exposed hammer and be of a type available in the 19th century. The Target rifle can be hammerless like an 1878 Sharps Borchardt and even of modern design as long as it shoots a period caliber.
No bolt actions allowed, even early ones.
There is a separate Cowboy Lever Action Silhouette event.
No duplex black over smokeless loads may be used in NRA competition. Only black or Pyrodex can be used for Silhouette, other "substitutes" appear to be allowed in Target shooting. Some of the outlaw matches like The Q will allow duplex or smokeless loads but not many.