Here in the state of Nebraska, the only game species left to hunt with a handgun is rabbit.
That's easy, hunt the rabbits.
Hunt rabbits, and the predators that hunt rabbits.
Join a pistol league and shoot indoors.
Work on your form,stretch the range out on your steel targets.
Starlings, English sparrows and rats are always around barns and feed lots A good pellet pistol/rifle for these.