One example, not built on top of a dating site but last.fm, tastebuds.fm is a social network/dating site based around music. Old discussion here http://news.ycombinator.com/item?id=1992801
They have an API and devs need API accounts. I don't know much about dating sites but I'm guessing they don't have APIs because exposing the type of data they store would be pretty creepy.