Obviously going back to a muzzle loading musket or rifle, as well as black powder brings about many issues as well. Hell, many modern gun designs would fail pretty quickly if black powder was used, since it leaves much more residue behind than modern smokeless powder. Though if a character wants a single shot (or few shots with multiple pistols) it would be a way to do it, like the liberator pistol the US Airforce dropped into France during WW2, it was meant for ambush to possibly get a better weapon.
You can have multiple shots with one pistol, as long as you don't mind it being small-bore, low-pressure, short
and heavy.
Obviously that's over the top, but four .35" barrels you could do quite sensibly.
Yes, it'd be smoky, very smoky, but it'd do well enough as a CQA weapon.
What'd be very tricky would be a rifled barrel. That's going to need some big facilities.
Smoothbore, straight-blowback, no safety catch, no fire selector, "angry tube" .22 LR you could make in a high school's metalwork department. Use Ruger 10-22 after-market 25-round magazines and
BZZZZZT goodbye, Jack.
A rifled barrel that's strong enough to take the pressure and stay straight and nice enough to improve accuracy over a smoothbore loaded with spherical bullets, though? Much harder to do, and/or very heavy.
You could mix the designs, if the ammo's available: take the design of the double-barrel shotgun, make it a 19-barrel:
... and have a plate with 19 pins on it, on a stiff spring, cocked by closing the gun and released by a single trigger, and you'd have a high-velocity 1.34 oz load of #4 buckshot with a very tight pattern ready to go. It'd take a while to fully reload. You might want to have a spare, loaded barrel cluster and a way to swap them out rather than shoving one round into one chamber at a time to reload each time, but if you only need to hit one target one blast's plenty.
You know what'd be a whole lot easier to make without a forge and power tools?
There are quite a few ways to "trigger" a crossbow, including that thumb-trigger or a ratchet barrel holding the string back and held back by the front end of an underside trigger.
The fletching can be paper, plywood, feathers, bits of the plastic trays of ready meals or even bits of string.
The arrowheads?
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Not like a few pieces breaking off inside the target makes it
less deadly, is it?