Personally, I don't think the 17 HMR is enough for coyotes. Having said that, if they were 50-75 yards max, and you were assured a head shot-I'd have no problem agreeing that the 17 HMR will do the job. Certainly the .308 will do the job-but will be very rough on hides-as well as more prone to richochet. If you have wide open spaces and don't care about hides, I'd use the .308 Win.
Ideally, you'd have a rifle to split the difference, but I know what it's like to not have the "ideal tool" for the job. Nothing wrong about shooting a coyote with a .308!