Your two best choices are probably going to be a .223 Remington or a .22-250. The .223 is cheaper to shoot, has better barrel life, and is adequate for coyotes out to about 325 yards. The .22-250 is about 500 fps faster with the same bullet weight, and will extend the maximum effective range out to about 400 yards.

You might looks at a Stevens 200 or Savage 110. Be careful buying used .22 centerfires. These guns are commonly used for high volume varmint hunting and may have the barrel already shot out.