People tend to forget there's LOTS of calibers.

Not sure if it'll work for you, but .17HMR is a light round (smaller than .22) and works up to animals about 40-50 lbs (think large coyote). Maybe bigger with good shot placment. Bad side is the cost of the rounds is kind of hight.

I know there's also single-shot .223 rifles. It's a bit peppier than your standard .22, you can find ammo everywhere, and it'll take down deer size pretty well. Ammo is fairly inexpensive, and you can buy LOTS of surplus ammo.