You can probably find an inexpensive bolt rifle that will manage a coyote just fine.
In fact, a quick browse around ImpactGuns showed a Remington 710 in .270 (a wee bit more than you need) for $352 and it includes a premounted Bushnell scope. Probably not the greatest glass ever, but certainly adequate.
.270 is also enough for deer should you ever want to take it hunting.
Its not as pretty nor is it as "polished" as its 700 series brethren, but for ridding your land of excess 'yotes, it should be more than adequate.
Then again, my uncle got one last year when it tried to attack one of his foals. A good shot with a .357 magnum (S&W Model 19) took care of the critter in fine style.