The 7.62x47mm will put a coyote down much better than your rim fire, no question.
Check local regulations about magazine capacity to see that you will be legal. In Arizona, you can use only 5-round magazines while hunting. The SKS has a 10-round mag, in factory format. May be hard to find a factory 5-round magazine for AK (you may have to modify one).
Oh, yes, be sure to use soft-point or hollow point bullets while you hunt; the fmj bullets will not have much affect on the critters.
Likely, you will find the SKS to be the more accurate. My SKS has a much better trigger pull (quality-wise) than any AK-47 that I have fired.
Hope this helps.