Kay,
most community baseball programs have scholorships for players who can't afford the fee, so first I would ask the coach or board of that league if they are available. Second many towns have summer recreation programs, have you checked that out, your town office or public school would be a good place to start. The goal of most of these programs is to make sure every child in the community can participate in summer recreation regardless of ability to pay.

Try a church league... free is tough to find in this economy. I agree with Coach Moore but sometimes there is a pride issue or some parks may not offer scholarship programs so you may want to do some sponsorship work yourself. Try approaching to some of your local businesses to find out if they'll sponsor your youngster... who knows, they may be sponsoring the next D.Jeeter.