Freakonomics co-author Dubner just peeked at professional sports dating life and didn't like what he saw. Granted, if you look at life through the lens of who appears in court, you're going to be very unhappy.
Were I an NFL coach, and I saw my team's personal lives getting out of control, I would be tempted to help them by getting together with other NFL coaches and setting up a dating agency. We'd prequalify a bunch of women and constrain their actions by contract before they even talked with the players (they'd essentially waive the right to sue the NFL, the dating agency, any current or past NFL player, coach, or employee). Nowadays, you could probably charge women to get into the dating agency.
I realize that gay NFL players would be an underserved market, but unless they were out, I don't think they'd participate for fear of privacy loss.