When I was at Pontiac Public Library I arranged for the local professional football team (Pontiac Generals) to come to our library and participate in the storytime. They donated tickets to an upcoming championship game for a prize drawing, too. I contacted the coach (a personal friend) to set that up. The coaches were looking for volunteer work for their team in the community so it was mutually beneficial. They are still around but the league and teams have been reorganized and renamed since then.

There was a soccer league that attended a Summer Reading kick off event, as well. I knew of them because some patrons were big fans of the team. I looked up the contact information for the PR department. There was also a performance team from the Pistons organization but I believe that was under a performance contract. I did not set that one up, though. 

My best luck with sports talent has been when I have stuck to the local teams and when I have known someone (or known someone that knew someone).