The Glock 19 is the standard sidearm carried by Detectives in the NYPD including Tony Caruso Jr. (Josh Groban) and Cora Vasquez (Monica Barbaro). Uniformed officers and FBI agents are also seen with Glock 19s.
Tony Jr.'s own Glock is at the center of the first episode "Who Framed The Good Cop" (S1E01), where it's used to frame him in an incredibly convoluted way for a murder.
SIG-Sauer P226
Some uniformed NYPD officers can be seen with SIG-Sauer P226s in their duty holsters.
Colt Gold Cup National Match
The NYPD rangemaster, Chet Finch in "Who Framed The Good Cop" (S1E01) is seen armed with a nickel Colt Gold Cup National Match when he discovers Tony Jr (Josh Groban) and Cora (Monica Barbaro) investigating the range for evidence.
Kahr K9
Cora Vasquez (Monica Barbaro) carries a Kahr K9 as her personal sidearm in "Who Framed The Good Cop" (S1E01). She nearly empties it and then passes it to Tony Jr, as he uses the last round in the chamber to hit Chet Finch.
SIG-Sauer P229R
The Bunny Mask killer in "What is The Supermodel's Secret" (S1E02) is seen using a two-tone SIG-Sauer P229R with wood grips and a silver suppressor to kill Mr. Monte. The gun is later handled by Belinda Mannix (Emma Ishta) and used against its owner. The gun seems to be missing its rear sight.
Smith & Wesson M&P9
In "What is The Supermodel's Secret" (S1E02) Tony Jr. (Josh Groban) is seen drawing a Smith & Wesson M&P9 instead of his usual Glock 19. This must be a continuity error, as it only happens in one scene.
In "Who is The Ugly German Lady" (S1E03), TJ (Josh Groban) can be seen with holstered gun next to him on his kitchen table, but instead of his usual Glock 19, it looks like a CZ P-10F.
Smith & Wesson 5904
In a continuity error in "Who Killed the Guy on the Ski Lift?" (S1E07), Tony Jr's (Josh Groban) Glock 19 briefly turns into a Smith & Wesson 5904 when he enters a hotel room with other police officers.
Donovan Demark (Dan Byrd) uses one in "Who Cut Mrs. Ackroyd in Half?" (S1E10).
P-64
One of the Lithuanian thieves at the restaurant in "Why Kill a Busboy" (S1E09) is armed with a polish P-64 pistol. He then uses it to kill the aforementioned busboy in the restaurant's kitchen. Big Tony (Tony Danza) identifies it as "Makarov automatic" (which would be somewhat correct) and that it ejects to the left, prompting Cora to look in a different place and find the spent casing used in the murder. The latter comment about the P-64 is incorrect, unless either Tony got the direction of the shooter wrong (which is possible, since the kitchen's doors were closed) or the shooter shot the gun upside down, which is a very unusual thing to do.
Very few handguns eject to the left (the Walther P5 being an example) and the polish P-64 is not one of them.
Revolvers
Smith & Wesson Model 36
An assassin in "Will the Good Cop Bowl 300?" (S1E04) is seen using Joey's Smith & Wesson Model 36 against him after a confrontation gone wrong at the bowling alley. When talking about the slug recovered in the victim's head, Cora (Monica Barbaro) refers to it as a 9mm, which is incorrect as the revolver is chambered in .38 Special.
Smith & Wesson Model 640 Centennial
Tony Caruso Sr. (Tony Danza) is seen retrieving what appears to be a Smith & Wesson Model 640 Centennial from his hidden safe in the wall in "Will Cora Get Married" (S1E08). He's later seen with it in his waistband and at the end of the episode to save Cora (Monica Barbaro) from Warren (Josh Segarra). He hides it afterwards, since a convicted felon is not really supposed to own a gun.
Submachine Guns
Heckler & Koch MP5A3
FBI agents in "Will Big Tony Roll Over" (S1E05) are seen armed with Heckler & Koch MP5A3 submachine guns with Surefire handguards.
Mini Uzi
One of the thieves in "Why Kill a Busboy?" (S1E09) is seen armed with a Mini Uzi
Shotguns
Remington 870
NYPD officers looking for Sherman Smalls (John Carroll Lynch) in "Who is The Ugly German Lady?" (S1E03) are seen armed with Remington 870 shotguns.
Rifles
MGC M16
An NYPD officer is seen retrieving an MGC M16 replica rifle from a gun case in "Who Is the Ugly German Lady?" (S1E03).
Colt Carbine
What appears to be a Colt Carbine variant is seen held by some police officers in "Who Is the Ugly German Lady?" (S1E03). Though only seen briefly and out of focus, the shape is mostly recognizable.
Colt M4A1 Carbine
An M4A1 Carbine without sights is briefly seen as an NYPD officer opens a rifle case in "Who Is the Ugly German Lady?" (S1E03). NYPD ESU officers are also armed with similar rifles when apprehending the two Lithuanian hitmen, this time with optics, in "Why Kill a Busboy?" (S1E09).