Ream your Cooper out to .222...you might have to change the follower, but that's no biggie.
My favorite varmint rifle is a Remington "build" using a .221 fireball reamed out to .222 Easy Peasy cause the deuce is the parent cartridge.

[Linked Image from i.imgur.com]

"...the left considers you vermin, and they'll kill you given the chance..." Bristoe