You could not exterminate coyotes if you wanted to.
Scott
Thats pretty much a true statement. Back in the 50's and 60's We could drive for miles down the country roads in Osage county and they would hang coyotes from every fence post, minus their ears. You got a bounty for each set of ears.
I finally got old enough to go with my uncle, and he rode mules. We ran them at night through the pastures behind greyhounds, shooting them when the dogs cornered them. There were hundreds of carcasses on the fence posts, and guess what....there are just as many of them now as then. Maybe more.
They continue to expand their range, with reports in Central Park in NYC. Don't know how credible those reports are, but Its been on the news.