I hunt that area alot. There are almost as many people tracks as Coyote tracks in that particular part of the state.
but, the same could be said for the area within 25 miles of Williams.
So people say that it's very hard and as AZDiamond says, they are well educated.
But, you can also take that as a challenge. I see it as an advantage. yes, the dummies are gone. Most of them are on the side of the highway by November. But, if you concider how most predator hunters hunt, you can take that into account and use it to make your hunting plan and do something they haven't seen and be very successful.
Also, i don't know how much experience you have, but hearing them and getting them inside 100yrds is a whole different game.. Driving out to an area where you "hear" coyotes isn't the same as an area that has lots of coyotes. It doesn't take many to make you think they are everywhere, when in reality they really are not. Take the advice or information from locals and ranchers with a grain of salt. They will all tell you out there, they are everywhere.. That seems to mean they see one every couple of days.
Good luck, and personally i leave the area's alone this time of year to give the little ones the most chance of getting bigger for me to shoot later.
I am not a rancher and they ain't eating my pets, I have to drive hours to get there, So i leave them alone now because if i shoot a wet female, i have almost certainly killed all the pups. I would rather shoot them too in the fall.
Good luck, and welcome