One of the places I would advocate that the Tigers look for pitching help is Japan. Today, 22 year old Junichi Tazawa has announced that he will not be joining the professional leagues over there and will instead be coming to the Major Leagues.
Whereas most pitchers who come over from Japan are well into their 30's, Tazawa's arm is fresh and should be able to withstand a multi-year deal. He evidently throws in the mid 90's with a forkball and slider. That sounds like prime reliever material to me, and this could be a piece of a bullpen that is sorely lacking in arms right now.