I would start by contacting game and fish. If that goes well, I would find out who your local government trapper is and talk to him around denning season.
I would also like to tell you about a couple books that would be a good source of info on this subject. One is The Clever Coyote by Stanley P. Young and the other is The Voice of The Coyote by Frank Dobie. Both can be obtained on amazon or any other book website.
Also, I would like to add that your comment about people with bi-polar being nuts is way off balance and completely wrong!!

If you will do your research on this like you did on a coyote as a pet you would understand that bi-polar is a actual medical issue. It is a disease just as cancer. It is a chemical embalance in the brain that is easily controlled by medications. It is usually passed down from one generation to the next and often times skips a generation.
The reason I know all of this is because I was diagnosed with bi-polar when I was thirteen.(I am 37 now) It is hard to make people understand this disease.
I believe you to be completely judgmental and not willing to take sound advice. There are a few success stories out there about coyotes as pets but for the most part it generally doesn't work out. I also believe that if it doesn't work out that people that try them as pets and turn them loose, cause alot of problems with the coyote becoming habituated to humans and causing more problems with coyotes attacking innocent children and adults. If things don't work out, I hope you will have the guts to shoot the thing where it stands and not let it effect your whole area. Just my opinion.