A guard in Stoker's estate fires a revolver at Bertie Wooster in "Safety in New York (or, Bertie Sets Sail)" (S3E1). The revolver appears to be a Smith & Wesson medium frame model, like Smith & Wesson Military & Police, but the ejector rod looks uncommonly short.
Webley revolver
A Webley revolver is seen in hands of Hilda (Harriet Bagnall) in "Bertie Takes Gussie's Place at Deverill Hall (or, Right Ho! Jeeves)" (S3E4). "Parrot's beak" grip and general size allows to guess it to be a model from Webley .455 Mk I to Mk V. During the scene Hilda's gun switches to a Colt-style revolver (see below) and then back to Webley.
Colt revolver
Hilda's Webley revolver in "Bertie Takes Gussie's Place at Deverill Hall (or, Right Ho! Jeeves)" (S3E4) switches to a Colt and then back to Webley. Colt Police Positive is a possible guess.
Compact Smith & Wesson
In "Lady Florence Craye Arrives in New York (or, the Once and Future Ex)" (S4E2) D'Arcy "Stilton" Cheesewright (Nicholas Palliser) holds a compact top-break Smith & Wesson (like Smith & Wesson Model 2 Double Action) during the dress party. Somewhat similar revolver is seen in hands of NYPD Capt. Corrigan (Sam Douglas) in same episode.
Various revolvers
New York police officers carry various revolvers (seems to be a mix of several Colt and Smith & Wesson models) during the pursue in a skyscraper in "Bertie Ensures Bicky Can Continue to Live in Manhattan (or, the Full House)" (S3E2).
Submachine Guns
Thompson M1921
Some guards in New York prison Blackville Island carry Thompson submachine guns in "Safety in New York (or, Bertie Sets Sail)" (S3E1). The guns are seen only in distance; Thompson M1921 seems to be a decent guess.
Shotguns
Double Barreled Shotgun
Double barreled shotguns are seen in hands of Tom Travers (Ralph Michael), Gussie Fink Nottle (Richard Garnett) and Bertie Wooster (Hugh Laurie) in "How Does Gussie Woo Madeline? (or, Hunger Strike)" (S1E4); Roderick Spode (John Turner) in "The Silver Jug (or Jeeves Saves the Cow Creamer)" (S2E1); some members of Roderick Spode's fascist group Black Shorts in "The Bassetts' Fancy Dress Ball (or, A Plan for Gussie)" (S2E2); and Sir Watkyn Bassett (John Woodnutt) in "Totleigh Towers (or, Trouble at Totleigh Towers)" (S4E5).
Single Barreled Shotgun
A member of Black Shorts carries a Single Barreled Shotgun in "The Bassetts' Fancy Dress Ball (or, A Plan for Gussie)" (S2E2).
Pump action shotgun
Some guards in New York prison Blackville Island carry pump action shotguns in "Safety in New York (or, Bertie Sets Sail)" (S3E1). Possible guesses for these shotguns are Remington Model 31, Stevens Model 620 or Stevens Model 67.
Rifles and Muskets
Percussion Cap Musket
In "The Bassetts' Fancy Dress Ball (or, A Plan for Gussie)" (S2E2) a member of Black Shorts (in center) carries an antique percussion cap musket, likely a hunting model.
Small caliber lever action rifle
A member of Black Shorts carries a lever action rifle in "The Bassetts' Fancy Dress Ball (or, A Plan for Gussie)" (S2E2). Due to its relatively small receiver and slim barrel and tube magazine it appears to be a small caliber gun. Browning BL-22 seems to be a decent guess.
Bolt action rifle
A bolt action rifle is seen in hands of a Black Shorts member in "The Bassetts' Fancy Dress Ball (or, A Plan for Gussie)" (S2E2). The bolt bears resemblance with Weatherby models but it's too vague.
Break action rifle
In "Cyril and the Broadway Musical (or, Introduction on Broadway)" (S3E3) Bertie Wooster holds a hunting rifle with a sniper scope during the hunt. It is supposed to be a break action weapon, a rifle rather than a shotgun as sniper scopes are quite rarely mounted on shotguns (but as this is a comedy, everything is possible).
Air guns
Air guns are used for target shooting on the fair in "Totleigh Towers (or, Trouble at Totleigh Towers)" (S4E5).