Welcome to the forum.
I've never tried this, but a few people on here have tried this or something similar.
I think the biggest thing will be getting permission or approval beforehand. Most parents probably won't mind and some (hopefully many) will buy photos from you...but you may run into parents who don't want you to shoot their children. If it's a public park, they probably won't have the legal right to tell you not to shoot...but you certainly don't want to make anyone uncomfortable or angry.
As for how to go about selling them or allowing parents to view them...I'm not sure. What works for one person, may not work for another. I think that a website with a password would be a good idea, especially if they could order prints directly off of the web site. A set up like that is possible but it probably won't be cheap or easy to set up.
I think you may be missing out by not wanting to do team shots or posed shots. Those would probably sell pretty well. You could even go as far as making up 'cards' for the kids...those would probably sell well.
Make sure that the league doesn't already have a contract with a photographer, because you might be stepping on someones toes.