I vote a +1 on the two gun plan. The coyote problem needs a much bigger gun than the small rodent problem, and it will be cheaper in the end to have two guns.
I would also suggest to do as much as practical besides the guns to control the problems, as such controls can work while you're not around to aim and fire. Plus if it ever comes into question, you would have done all you could to control the problem without shooting anything.
I live in the north east bay area, next to undeveloped open space, and like you we have coyotes, raccoons, pocket gophers, rats, hawks and huge horned owls. No voles though. We also keep chickens. The best defence I have found is "de fence" that goes around the chicken yard. I put monofilament mesh netting over the whole top of the yard, 4", 50x50 feet, strung from fence to fence and up above rope tied to 8' rebar tripods in the middle of the chicken yard. That keeps the coyotes, hawks and owls out. For the raccoons, I lock the chickens up at night in a sturdy coop (Eglu from Omlet.us ; they even have a light-sensing door that will close at night in case you come home late - _very_ CA techie). I bring in the chicken food bin every night so that the rats don't get any to feed their numbers. For the pocket gophers, my wife likes the "gopher gasser" smoke bombs as she is more into demolition and pyrotechnics, and I like the traps: the Macabee size seems to work well for those little gophers we have here in CA. Remenber to tie them to something ouyside the hole. And every gopher snake the neighbors screech at gets relocated to my backyard. (Maybe it is the same snake, over and over? It _is_ getting bigger each time.)
Regarding the guns, I can't advise for the 'yotes, but have you considered an inexpensive multi-pump for the rodents? They are quite accurate at your 10-20 yards, and it may even pay for itself by the time you factor in the cheaper .177/.22 ammo. My Daisy multi-pump is my go-to for rats, as I can match power to the backstop, and a bigger multipump like the Dragonfly or a Crosman 397/2 would also handle squirrels, if they ever become a problem. A CO2 gun would also work as it doesn't get that cold in the South Bay. If I were to $pend on a ratting setup, I'd get a cheaper gun and good IR nightvision scope, like an ATN or such. Juggling flashlights, pumping and fumbling pellets all at the same time gets old. I have one of those $100 IR cameras with light that attaches to a regular scope, and I'm glad I don't have a real rat problem because that setup bites runny rodent droppings.