I feel that coyotes are a separate class of predator compared to bobcat and fox, and I like a somewhat more authoritative cartridge for coyotes than for the other two.
For coyotes I'd recommend a .22-250 or a .243 in a bolt action rifle, or a 6.8 SPC II or 6.5 Grendel chambered AR-15.
For fox and bobcat I'd go with a .17 Remington to a .223 in a bolt gun, or an AR in .223 or .204 Ruger.