Check your state laws, you may need to have a hunting license to take them. It would suck to have your hunting privileges revoked because of something stupid like that.
Edit:
I just checked the regulations for your state (very easy to do online) and found that you have to have a small game license to shoot "vermin" including Coyote. If you have a big game license it's legal to shoot Coyote and Forest Grouse only, for all other you still need the small game license.
The Regs can be found here. Protect yourself and read them.
Washington Hunting Regs
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