Coyotes are indeed a nuisance, but normally not dangerous.
Highly intelligent, they avoid human contact but enforce canine rules with their teeth. A
majority of so called attacks are in defense of their den and pups. Find the den, capture the pups, then use them for bait to live trap and remove the adults.
Feral dog attacks on livestock blamed on coyotes don't solve the problem either or protect the livestock. Coyotes normally forage on small animals like cats, chickens, rabbits and new born animals (fawns and lambs). They're absolutely content with scavenging trash. In Arizona, we protect Pronghorn fawning with aerial gunning from helicopters. The Coyote removal is short lived as the population numbers return after 6 to 8 weeks via immigration. During that time, the fawns strengthen and then can run 50/60 mph to escape and are fine. Wolves will run Coyotes effectively removing them but usually not available as an option. Poisons will work but kill more non-target species like dogs than Coyotes. That's why we shoot from the choppers. I hate saying this but wildlife management officials are often not as smart or adaptable as the Coyotes and inept at Coyote management.