I wouldnt use a .17 on coyotes and the .22 mag is still a little small for yotes as well, but is better than the .17 for yotes, unless you head or neck shoot them.
The .17 is a bit destructive on small game at close ranges so head shots would be the ticket for closer ranges. However the .17 is extremely accurate at 100 yds. So much so that when they came out they demolished every rimfire in 100 yd competition shooting so they designated a class for themselves.
The .17 is a long range small game gun, it is what it is. Its not a varmint round.
I have one in a marlin and it shoots awsome, the savages are just as good, pick one you like and buy it.