Eli McCullough (Pierce Brosnan) carries a Colt M1911 chambered in .45ACP on his right hip, with a double spare magazine pouch on his left. Historically this should be the original 1911 variant as the 1911A1 was not introduced until 1924 (9 years after the events portrayed in the series).
Revolvers
Smith & Wesson .44 Hand Ejector 2nd Model
In Season 2's premiere "Numunuu" (S2E01), Ulises Gonzales (Alex Hernandez) in 1988 is seen taking out what appears to be a Smith & Wesson .44 Hand Ejector 2nd Model . The grip is engraved with the name "P. McCullough", making it likely the revolver used by Pete McCullough (Henry Garrett).
Single Action Army
Some of Sheriff Moses Dart's deputies draw their Single Action Army revolvers in "The Blind Tiger" (S2E03).
Rifles/Carbines
1893 Spanish Mauser
Some soldiers are seen armed with Spanish Mauser rifles in Season 2's premiere "Numunuu" (S2E01).
Winchester Model 1907
Eli McCullough (Pierce Brosnan) and some of the ranch hands use a self-loading Winchester Model 1907 chambered in .351WSL as their primary long guns.