Well, realistically, if you give away your widget, it promotes the sports team, it's clear the widget isn't affiliated with the teams or leagues, it doesn't portray the teams in a negative way or associate them with something negative then *maybe* no one will care. It would be infringment, but maybe no one will object.
If you want to do it right, though, you've got to get permission. I have no idea how you'd go about that. Contact the leagues' marketing offices? There might be some straightforward way to do this. I mean every newspaper in the country might want to display team logos along scores and schedules, and you are looking to do the same thing.