How about a dark horse candidate? For example, I was looking at the 34th Congress, and found a couple interesting choices:
Senator Richard H. Brodhead of Pennsylvania - While a northerner, his wife was one of Jefferson Davis' nieces (he even named one of his sons Jefferson Davis Brodhead). Like Franklin Pierce, it seems he would a northerner with a soft spot for Southern interests.
Senator Isaac Toucey of Connecticut - this one's a pretty obvious choice considering OTL, he was a governor of Connecticut, Attorney General, and a senator. He was a member of Pierce's faction, and a New Englander. Buchanan appointed him because of their history in Polk's cabinet, and to appease the said factions.