I trust the .22 Magnum and the .17 HMR out to 100 yards, maybe 125. Many will say they have taken them at longer ranges. I would trust the .22 LR out to 50 yards with proper ammunition, some might say 100. Getting a coyote within 50 yards is a trick though.
The Marlin XL7 or XS7 is a better rifle, IMO, than the Savage Edge (now called Axis) for a little bit more money. So is the Stevens 200 (made by Savage). The problem with the Marlin is ammo cost... it doesn't come in .223 or 7.62x39. The Savage and Stevens don't come in 7.62x39 (more on that later).
By far the cheapest ammo going right now is 5.45x39mm (like $120/1000 rounds) and you might find a rifle in the $350-$400 range. The 5.45x39 has plenty of power for coyotes, and hollowpoint varmint ammo is available from Wolf for ~$5 a box of 20.
7.62x39 is the second cheapest ammo,(the .223 is too much for squirrels, about perfect for coyotes, same goes for the 5.45x39), and since he already has a .22, if there is any chance he will be deer hunting, the 7.62x39 would be capable of it with the correct ammo (assuming it's legal to hunt with it in your area). So I'll go back to my recommendation for the Rossi in 7.62x39, or an SKS.
With my SKS I would be more than comfortable taking deer and coyotes at 150 yards. With the Rossi (and if I put a scope on it) I would stretch that to 200 yards. Rossi comes with iron sights so a scope could come later.