If you're talking a T/C Contender or G2, your only real option is the .30/30 based on your criteria. If you're willing to step up to the Encore, there are plenty more offerings that will do the job. Edited to add: Oops, no it's not. A .44 Magnum would do the job well, too, and a .357 Mag will work if you pick your shots. A 10" 10mm barrel may be the ticket here, too, though I wouldn't call the ammo "commonly" available.
With the Encore, you can get everything from .243 on up that will do the job you ask, though a .308 or .30-06 might be more in line with what you want. I have seen some Wal-Marts carry 7mm-08 ammo, and if your local gun shop doesn't carry it, they're messed up. .260 and .280 Remington would work well, as would the .270 Winchester.