Yes you can, but it has to be during the big game season. This is from the 2008 small game regulation book.
5.
You can hunt coyotes without a license in big game seasons if
you have an unfilled big game license for the same season and unit.
You must use the same method of take for coyotes as your big game
license allows.
A small game license is $21 plus stamps. I always buy the combofishing/smallgame license for $45. But I see your leaving the state soon so a 1 day smallgame license is $11.
Or find permission on private land and shoot away.