Well, it is obviously a metallic cartridge-firing breech-loading gun, so that means it can't be older than the middle (probably the last quarter, really) of the 19th century. But smokeless powder cartridges were not common until about turn of the 20th, so you've got a ~50 year window where many black-powder cartridge arms were made.
The exposed hammer design is reminiscent of an early design (very similar looking hammer arrangement to a percussion-cap ignition muzzle-loader). But that's not really a solid point of reference.
The condition of the bores appears immaculate, which might suggest that it was designed to fire more modern propellants (black powder is corrosive) but I would really want to see the right proof marks.
Getting chamber casts would also be a good indicator. Some cartridges were only popular in certain decades, and some weren't invented until smokeless powders came on the scene.