Without a motion camera it's more difficult, but not at all impossible (or even all time consuming).You simply have to have patience and understand your target, as most wildlife photographers do.
In this case it would be easiest to find in the wide open plains and deserts of the southwest, you can see them from very far away and the populations are quite abundant.
If that's not a possibility, ask around with those associated with your local wildlife (DGIF, Biologists, Wildlife Rehabbers, hunters etc.) and find a coyote hotspot, begin baiting or watching coyote trails (found through your or others surveillance) and waiting until they pass by. A motion activated camera will give you a good idea of what times will be most likely for a sighting.
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