Jerry (Joseph Cortese) pulls a Mauser Model 1934 and attaches a suppressor when confronting Bernie in his office. Bernie's bodyguard also carries one in his pocket.
Astra Constable
Marley (Keith Davis), the hitman that eventually finds Serge and Joe, uses a Astra Constable throughout the film, often suppressed.
Serge (Bobby Alto) carries a M1911A1 with white grips, which Joe (Joe Pesci) chides him for having, claiming it can "go through six people."
custom shotgun/rifle
The hitman gets a custom 18-inch barrel shotgun that fires a shotgun shell and a rifle bullet, using it during his confrontation with Jerry.
It doesn't make it custom, it is a O/U rifle/shotgun, I own a few actually. - Gunmaster45
The seller/manufacturer mentions in the scene that he made some modifications (although considering the low budget of the film, it's doubtful that any were actually made.)
double-barreled shotgun
Jerry uses a double-barreled side-by-side shotgun during his final confrontation with the hitman.
M2 Carbine
One of the hitmen during the finale uses a selective fire M2 Carbine with extended 30-round magazine to kill Jerry.