Has Billy ever dated anyone other than Teddy? Does Eidolon count? What about Teddy? I haven't kept up.
The short answer is no, not that we know of. Billy and Teddy were introduced as a couple in Young Avengers (2005), and they've never really broken up or had any other relationships since.
Their relationship wasn't explicitly confirmed until #7, and the original series was never totally clear as to whether they were already together at the start, or if they became an official couple sometime off-page. Recently, however, the King in Black: Wiccan & Hulkling tie-in established that Billy and Teddy did, in fact, meet at school and begin a relationship prior to joining the Young Avengers.
Neither character has ever indicated that they had any previous relationship experience. In Children's Crusade: Young Avengers, which is a single issue one-shot, Billy mentions that he used to make out with a classmate named Jimmy Stidham, but he doesn't say that they were dating. Teddy had a fraught relationship with a classmate named Greg Norris, who knew about his powers and basically used to take advantage of him. Some readers have interpreted this as a romantically and/or sexually charged abuse situation, but that's not strictly canon.
I don't think that their relationships with Eidolon and Goebig should actually count, but it was interesting to see them with different partners! Maybe if Hulkling & Wiccan had been a better comic, I would place more significance on those relationships, but the story was simply too shallow and too rushed. I know that Trujillo is writing another installment at some point, and while I can't say I'm looking forward to it, I am curious about Eidolon and Goebig and I want to see more of them. I thought it was actually very clever to pair Billy and Teddy off with people who they share more direct experiences with, and I'm curious to see what kind of dynamic they'll have in the "real" world.