Hey Jeff,
If you just want to hunt coyotes, you can get a general nonresident hunting license for $58.50. But, if you want to hunt bobcats, it looks like you have to get a full-fledged nonresident furtaker's license for $176.50. I'm not sure, but I would imagine you'd have to take the trapping test in order to get that. (That test is a one-time thing though). I'm just looking at the front of the Furbearer regulations pamphlet, and there's no provision for a non-resident furbearer hunting license. You'd then have to get the bobcat record card as well.
So...it would be pretty expensive, and a hassle as well. If you want to talk to someone at ODF&W, you can call (503) 872-5275.
-dan