First - from my experience with Savage - your 4-5" groups is way out of the norm. Before you go and dump the scope, even thought isn't a very good one, take it off and check to make sure the bases are tight. Reinstall and check the ring screws to ensure they are tight.
Next - I assume you don't reload as this is your first 'powder burner' is to try different types of ammo to see what one your particular rifle likes the best.
Clean your rifle well after each shooting session with a good quality powder and copper solvent. using a bore brush and patches. The rifle will shoot better after it get a couple hundred rounds through it.
Lasty, for coyote hunting, if you shots are going to be normally long, I would recommed you getting a scope in the 4-12X range. Depending on your financial situation - get the best scope you can afford. Leupold, Burris and Bushnell are reasonably priced and are pretty good quality scopes.