There are a couple of guys out there that make airguns in much larger calibers (like 30 and 45), that are charged off of scuba tanks.

I've got a little benjamin in 177 cal that has taken care of its share of rodents.

There's also a neat little load you can do with a 38 special or 357 magnum called a "cat sneeze" round. This is a 38 case with a OO buckshot as the projectile, using only the magnum primer and a few kernels of bullseye as propellant. Done right there's just enough pop to get the ball out of the barrel with 2-3x more velocity than a slingshot (but a heck of a lot more accurate), and it's got enough momentum to drop a rodent in its tracks at a reasonably close range.