We're landowners and what wolfhunter said is right on target. The difference here is that coyotes are the last remaining thing that I can hunt. I get too much $$$ for my antelope permits, I'm booked solid all summer on prairie dogs, and so forth. So, permission to hunt coyotes? Negative, sorry. But, I will point you to some other people you can go ask.
The one thing I have to add to what wolfhunter said is "Don't overtalk". I've met SO MANY people who talk the talk but don't walk the walk. The more you talk, the less inclined I am to believe you. Therefore, just ask a few simple but important questions "Gates- how do you want them? Dead coyotes- where? If I see anything that doesn't look right, call you?" Then SHOW me.
Another thing that irritates me, might not irritate other people, is when guys "talk down" to me. Some people seem to think that because we live out here that we're dumb illiterates. Umm.... wrong! In whatever you do, hunting, work, whatever, I think it's smart to find out where the person you're talking to is, and then meet at his level. If he knows more than you, learn something. If he doesn't, shut your mouth, unless he recognizes that you know something he doesn't and asks you for solid information. Talk to people like they're your peers, not like you're the know-it-all.
This goes with offering help. If you offer help, it's best if you know what you're doing. A guy that's never built fence before really isn't much good to me. But, if you're a good welder and are willing to offer your services, yessir!!! Or if you work at an auto parts store and can offer me either a discount or advice when I need it, that's valuable. Whatever you do, offer it. Toss it out there like a slow pitch and see if they swing. If they don't, let it go. If they do, proceed. Just don't be arrogant.
I have permission to hunt neighboring ranches and, believe me, I take my own advice. I hunt on a horse ranch and I find out where the "wild" horses are so I can avoid them. When I'm at the house, I look around for piles of dirt that might need to be pushed around and offer the use of me and my skid steer. I'm good with computers and used to do tech-support professionally- if the topic ever come up, I offer my services. I ask if there are any particular areas they want me to hunt- any problem coyotes?- any areas they want me to avoid- the wild horse pasture, for instance. I send them pictures from my trailcam and if they like them, I keep them posted with interesting stuff. An important thing to know is "Where should I park?"- on the road, on the grass, look for turnouts? Some ranchers are VERY particular about driving on the grass, others not so. And so on...
Good luck!!!