One hundred and fifty years ago, coyotes were only found in Arizona, New Mexico, Southern Colorado, Southern Utah and Southern California. As we began to remove the higher predators (mountain lions and wolves, mainly) they began to spread. They have now been spotted in every state in the Union save only Hawaii (they can swim, but not that far). They've even trapped them out of Central Park in NYC, where they had to walk across one of the bridges to get there.
They are the second-most successful predator on the North American continent (we're first, folks). They are successful precisely because they are non-specialized. They will eat just about anything, small dogs, cats, garbage, dog or cat food, mice, rats, small snakes, vegetables (right out of your garden). The Navajo will tell you that a coyote can tell a ripe watermelon from one that isn't ripe yet and break open the ripe one and eat it.
The only successful coyote abatement project yet known was the re-introduction of wolves into Yellowstone. Prior to the re-introduction of wolves, coyotes had taken over Yellowstone, but the wolves quickly reduced the population by about 75%. Now the coyotes only live right around the populated areas of the park where the wolves don't go. The Lamar Valley, where the wolves are the most at home, is free of coyotes.
They are the second fastest land animal in North America (for short distances only, the pronghorn can outrun them). Wolves can run them down because of their superior stamina.
They are adaptive breeders. In the pack, if the local area is "full" (it has a full complement of coyotes based upon the food supply), only the alpha female comes into estrous and she will only have one or two pups (the whole pack will feed and raise them). Just enough to offset natural mortality. If you shoot down or trap down the local population, every adult female in the pack will come into heat, they'll all produce a litter and they'll pretty much immediately fill the range back up within twelve months. How they do that is not well understood, but it is well documented. That is why the old Federal programs to "eradicate" the coyote in rural areas of the West was and is a failure. If you do manage to kill off the adults, you will get pups from the surrounding area who will quickly repopulate the whole place and pups will be even more likely to kill livestock because they didn't have adult pack members to teach them better manners.
As noted, they are not particularly afraid of people. They become less so because idiots leave out dog food or put it out on purpose 'cause they "think they're cute." I throw rocks at them when I see them, just so they don't think humans are entirely harmless.
The best book on them is God's Dog, by Hope Ryden.
I live in an urban neighborhood that has two packs (yes, I can tell them apart, the numbers are different and the individuals are different). I can carry a firearm, but I can't discharge it (too close to residences), so I carry a small bear spray when I walk my dog (although she's not really at risk, she's a 114-pound Rhodesian Ridgeback — she just looks at them and they just look at her and then everybody goes their separate ways). I'm more afraid of the Javelinas we have, they're dumb and almost blind and will charge just about anything if they are challenged or surprised and they can do a lot of damage to a dog or a person.
Just so you understand my interest, my screen name, Chuhhuniban, means Gray Coyote in Tohono O'odham. I've watched and lived around them all my life. I like coyotes, but I don't have any problem with people hunting them or destroying them when they become a nuisance. I'll just tell you that you are about as likely to get rid of them as you are to get rid of cockroaches. You can thin 'em out for a while, but like Aah-nold, "they'll be back."
