One of the best ways I have found to consistantly kill coyotes is make rounds to 2 or 3 locations. Setting up a bait station for coyotes and utilizing cameras. Adding bait more and more regularly as you see one site getting hit. Then focus on that spot. Have a blind, stand or other means of cover to overlook your bait. Sit the last few hours of light. And first few hours of daylight. In a matter of a few days sets you have high probability. This is legal for coyotes specific and very effective. Just sourcing different bait to have enough to replenish is biggest concern. Be respectful of areas and keep bait out of site of non hunters.
Pierce county is tough as there is little public lands available for coyotes. Without an access pass. JBLM has tons of coyotes but hate dealing with there program to try to hunt them. Ideally a private farmfield is best.