With the parameters of legal for deer in WA, factory loads and no need to save fur, I'd go .243 or 25-06 with a 2-7 scope mounted as low as possible. The low mount is to keep the bullet path as close to line of sight as possible for medium range and close shots through small holes in your wet coastal brush. 2-7 gives a pretty good sight picture from close to more than 300 yards for the open clear cuts. Once in awhile a coyote will be too close to focus on with 2 power but they die the same when blurry. For factory coyote bullets with no concern for fur I'd go with light, fast and frangible.
If you are a long ranger, make it a 6.5 Creed with a 6-18 or higher 50 or 56 mm scope with a bipod-- and kick the close ones.
Added: as said by others, start calling now with the .308 rather than wait for a more specialized rifle. It is prime time to call, with naïve young adults just now blundering about on their own. It was my experience shooting coyotes with 30-30, .22 and 30-06 that led to my choice of a heavy barreled 6mm for coyotes that would also be good for deer. It is.
