You can find some powerful airguns, but you won't come close to finding one in .22 caliber that is anywhere near as powerful as a .22LR firearm. You would need to look at the big bruiser air rifles.

Something like this: http://www.airgunstyle.com/big-bore-dragon-claw-pcp-pellet-air-rifle-050-cal-p-23946.html

Pellets for it are NOT cheap though: http://www.airgunstyle.com/air-venturi-5...nly-p-2341.html

And you'd have to find a setup to charge it with.

Powerful air guns are not silent by any means. A subsonic .22LR round in a rifle is quieter than many high power airguns. However you can get some precharged pneumatics with silencers built in.

Like this one: http://www.airgunstyle.com/airforce-talon-ss-pcp-pellet-rifle-022-cal-p-793.html

But this Talon model is not in the power class you are wanting.

I would recommend you just get a .22LR firearm. Air rifles are fine for hunting squirrels and such, but if you want to go much bigger than a small rabbit without upgrading to exotic air guns, you're really in firearm territory.