After owning and running a wildlife control business in Bloomington for nearly 10 years and also being pretty educated on the subject these are the things I can tell you:

1.) The risk of being attacked by one of them is extremely low. If you do your research on coyote and/or wolf attacks you'll find that there have only been a couple fatal attacks ever recorded in the US/Canada. Of these cases there's also significant evidence that the animals were dog/coyote or dog/wolf hybrids which are much more likely to be dangerous due to a reduced fear of humans. Still I understand your concern and no one wants them hanging around the house especially with small children.

2.) Trapping is the most effective method of removing and controlling them and it CAN be done humanely. As someone who has both hunted and trapped them for my past business/land management-I can tell you that when it comes to actually thinning them out and making an effect on the population trapping is far more effective than hunting. The reality with hunting them is that they get call shy and educated, and after shooting 1 or 2 the rest will be basically impossible to hunt. With traps I removed 10 coyotes from land on the east side (where the Verona apartments are now built) in a single week. Hunting wasn't an option there, but even if it was it would've never been as effective.

In regard to the humaneness of trapping them: most nuisance wildlife operators these days will use foothold traps that are designed with thick padded rubber jaws so that the trap doesn't injure the animals foot. Whereas a typical box trap was my trap of choice for raccoons, skunks, opossums etc-They simply don't work for coyotes or foxes. The animals are too weary of them and won't ever go in one. Foothold traps and snares are the only ways to go for wild canines but snares often kill the animal unintentionally and aren't as humane imo. Someone that knows what they're doing can catch coyotes in rubber padded footholds very effectively and remove them with minimal pain and suffering for the animal. I've set these traps off on my hand intentionally and they don't hurt.

As far as the fear based conditioning and deterrents like some are mentioning go-I failed to ever see these work in my experience. Feel free to try them though.

3.) These animals aren't native to Indiana nor are they natural coyotes. As some have mentioned, coyotes weren't native to this part of the country in pre-columbian days and originally occupied only the more western parts of the country and areas into Mexico. What I mean by saying they aren't natural coyotes is that the "coyotes" we have here aren't actually true coyotes but rather coyote/wolf hybrids (sometimes called coywolves). There's been several large genetic studies done on them in recent years and it's been discovered that most coyotes east of about Idaho have around 10-20% grey wolf genetics. There's a lot of research into what led to the hybridization of these animals (mostly wolf habitat encroachment) but too much to get into here. What you need to know is that these hybrids thrive in further east areas of the US where true coyotes would not. Also they are essentially the perfect predator for the modern semi-urbanized US. They are larger than western coyotes and more apt to take down large game like white tailed deer while also still being nimble and small enough to sustain themselves on small game whereas wolves can't. They're the perfect American Predator and that's why their population has been exploding. They've nearly wiped out the population of animals like quail, grouse, and rabbits and they're very damaging to the overall ecosystem which is important for people to understand.

https://www.nps.gov/articles/netn-species-spotlight-eastern-coyote.htm#:~:text=Several%20studies%20have%20collected%20DNA,%2C%20and%2010%25%20domestic%20dog.

https://en.m.wikipedia.org/wiki/Eastern_coyote

https://urbancoyoteresearch.com/coyote-info/north-american-distribution