Last year's contest was an unexpected shootout with Duke that was fun, plain and simple. At this point the other opponent is up in the air. Projections have ranged from Miami, Duke or North Carolina in recent weeks. Honestly I would be happy with any of those matchups being it for the Bearcats.
That being said North Carolina would seem to be the pick. Bowls generally shy away from rematches, be it from the regular season or the previous year which crosses out Duke. Miami is obviously the biggest name of the bunch, even if they haven't played up to it in a while. But the Bearcats have a game with them scheduled for next October, a game which ESPN will have the rights too. ESPN has an ownership stake in the Belk Bowl, and would gently nudge them away from setting up a game for them to broadcast which they will get the rights to regardless in 10 months time.
Which leaves North Carolina, thats my guess.