Gotta agree with Sheridan... At the ranges a .22lr is effective, a shotgun with buckshot is even more effective.

If you only have a .22lr, then yes, a .22lr will work at short ranges. Like some of the other guys, I've used a .22lr for trapping coyotes for years, but these shots are usually within 10yrds. I've also used a .22lr for hunting coyotes, but only at a range where I could guarantee clean head shots. Although, I have recovered coyotes shot within 75yrds that had .22slugs squished against the outside of their skull (Thank God for semiautomatics).

It'll work until you can get a new rifle. A great option for a budget coyote rifle is an H&R Handi-Rifle in .223 or .243win for about $250...