i wouldnt even bother with it for coyotes. you'd be better off with a shotgun if that's all ya got. of the two guns you mentioned i'd have to go with the 7mm-08, just use the smallest bullet you can get for it that your rifle likes. then take it out and use it to actually kill some coyotes, and at the same time you'll be practicing with your deer rifle or whatever else you use it for. save the 17 for the milk jugs.