Joss Merlyn (Sean Harris) holds a New Land Pattern Flintlock Pistol with the flat heel of the grip, typical for the East Indian Pattern. The pistol is definitly a modern replica, may be a non firing one.
Sea Service 1756 Flintlock Pistol
In the climactic scene Vicar Francis Davey (Ben Daniels) holds a Sea Service Flintlock Pistol. The screen gun is a non-firing replica that slightly differs from the original pistol. When Davey "fires" it, he only cocks the hammer and presses the trigger, without any imitation of loading. Flashes on the lock are seen but the pistol doesn't produce muzzle flame. Very similar model can be seen in Henry Krank catalogue (63P) but the manufacturer isn't mentioned.
Heavy Dragoon Flintlock Pistol
Due to continuity errors, Davey's pistol several times switches from the Sea Service to the Heavy Dragoon pistol and back againt. This Heavy Dragoon pistol isn't seen "firing". A long flintlock pistol that is seen in hands of a customs officer is also supposedly to be a Heavy Dragoon (no belt hook can be seen, so it's hardly a Sea Service).
Double Barreled Flintlock Pistol
During the prison break, Jem Merlyn (Matthew McNulty) takes two Double Barreled Flintlock Pistols from the customs officers' armory. He uses this guns in the climactic scene. These pistols are definitly modern replicas, may be non firing ones.
Unknown Long Guns
During the ambush on the wreckers' gang, customs officers fire some long guns. They are seen at great distance and cannot be identified. Flintlock Muskets would be correct weapons for this scene, but it's unknown what guns were used.