I feel like Detroit/Chicago is one to some extent at this point. Not historically of course (see my avatar) but the Hawks were irrelevant from the mid 90s to just a few years ago and hatred or dislike for Chicago gave way to a kind of "aw how sad to see another Original Six team fallen on hard times" type pity, I remember Wings fans admitting to rooting for the Hawks on their Cup run..which doesn't sound like a real rivalry to me.
A few more playoff match-ups would probably change that sense on the Wings side, especially if they are close and there's controversy, things not going the Wings' way. Right now though for being the Wings' best traditional rivalry in the West, there just isn't all that much bad blood.