I use my Ruger 10/22 For just about all small game and plan on using it on coyotes( for trapping). But for calling coyotes these are not the right bullets(like everyone said above)
I shoot 32 grain .22 bullets and at 100 yards they lose half of their kinectic energy and drop about 14 inches.(however just yesterday I sighted it in at 100 yards and shot a 2" group after 40 shots, also I had to take the scope 20 clicks up from it's previous setting which was 25 yards) So the answer is "yes" you can but no you really shouldn't.
Just my opinion †hough I have heard of people shooting coyotes and 200 yards with .22's