[fredtheobviouspseudonym]

As High Tech noted, air rifles were a functional technology in the late 18th century.

Not much good for battle but use of even cheap air rifles can allow practice of sight picture, trigger control, breath control, and other talents that can save a lot of time in training with gunpowder weapons. Pellets are cheap and easy to manufacture (cast, then swage for proper diameter) and air costs a lot less than even black powder. Pellet are also smaller (c. 7-10 grains a round -- vs. 55 for a .22 Long Rifle).

I also suggest that a Remington Rolling Block is a good deal -- should be able to use a very crude cartridge case that would limit the cost in $ and high tech. See the Snider for an example of a case that has a cast base (IIRC) and a "body" made up of would [typo -- meant to say "wound"] strips of brass.