Depends upon what you want in features, and how far away you want to be able to shoot coyotes.
$100 would get you a serviceable rifle. You could spend up to $1000 on a quality rifle. You could spend a lot more than that on something fancy, but it would be a case of diminishing returns.
A local sale would probably be best, in terms of avoiding excess Federal paperwork.
You might want something better than .22 for coyotes, though. .223Rem (aka 5.56mm) is a popular "varmint" caliber. .30-30 is a old-school deer cartridge, but the lighter loads would be workable for coyotes, without making the mess a higher-power load might.
Pistol-caliber carbines (a small rifle that fires a pistol-caliber round) are also popular. Something like a Kel-Tec Sub2000
is interesting, because it folds up for storage.
A smaller shotgun is also an option. Something in 20-ga, loaded with birdshot, would be effective. Plus, since you folks seem to be the unwilling hosts of visits by the blue-light gang on occasion, a traditional-looking shotgun (wood instead of plastic, maybe even a double-barrel rather than a pump, etc.) is less "scary" than something "tactical" in appearance. Less likely to help them work themselves up so they can engage in their antisocial behavior without guilt...