That's where many of us started. However - the diminutive .22 LR loses its effectiveness almost by the foot. Though it's all I had available when I was a kid running a trapline, my shots were generally less than 25 yards and typically head shots.

Given that coyotes are crafty little buggers, you're not going to get them in close enough for the .22 to be other than marginally effective unless you've got one in a trap.

Nonetheless, there's a lot one can learn about coyotes with a .22, one of the earliest lessons will more likely than not be "I need a centerfire."