For Coyote, AR's and Rifles are legal statewide with no capacity limits on magazines.
What has happened to where you thought about this?
Wraithen is correct. This is true in more heavily populated areas. However the area you are talking about you are good to go with any statewide legal firearm.
What do you mean about "This is true in heavily populated areas"?
Many parts of the state (generally near heavily populated areas) are "firearm restricted" which means that centerfire rifles are not legal for hunting. For example, several parts of King County are "firearm restricted". All of San Juan County is firearm restricted, and so forth.