I have a AA TX200HC in 22. I did have it tuned and put a Hawke 2x8 on it. It's taken out a few racoons, crows, and many squirells.
With the airgun I found you need to practice quite a bit to make sure you can shoot in quarter sized groups consitently. Pellets, flinch, non leaded up barrel all lead to wild shots. It takes a bit of time to get it right and head shots are a must (get a good scope).
Check out PyramidAir for used airguns too, maybe you'll find something. If you could expand your price a bit :
http://www.pyramydair.com/s/m/Beeman_HW97K_Elite_Series_Combo_Air_Rifle/1886This and the AirArms are all my UK brothers will use (although their challenge is to be under 12ft/lb in order to be compliant) and got me looking at this quality of airgun.
Wardman.