I used to hunt coyotes for pelts back in the 1980s. I would recommend a different rifle than the 30-06 if you want to save the pelts, a 30-06 will disassemble a coyote pretty quickly. I used a 22-250, but that is a lot of rifle too, and can damage pelts unless you are very picky about your shots. A 223, 204 Ruger, or 17 Remington would be my recommendation. I always shot for the head on a stationary target or one moving straight away. Broadside shots went to the neck or shoulder.
Hunt early morning and dusk. Buy an electronic caller, you will have better luck right away. Walk into your area, set up facing into the wind with some structure behind you to break up your profile, wait 1/2 hour, then call for about 15 seconds. Keep your eyes open and watch for movement. Wait 1/2 hour, then call again if there is no movement. If you hear the coyotes yipping after you call, you're busted, might as well move on. You will educate quite a few coyotes at first, later you will get good enough that you can go several setups without being busted.