League Lab makes your site pretty friendly to Google and other search engines by default, but they will definitely take a while to warm up to you. As you get more pertinent content published and more daily visitors, your search visibility will get better and better. It also really helps if you can get established sites to link to you. If all else fails you can buy traffic with something like Google AdWords.
Another thing that can help is to put your site on a domain that includes your geography name and says what you do (springfieldadultsoftball.com) rather than using an obscure name on a League Lab subdomain (sasbl.leaguelab.com). This is easy to do and well-worth it if you end up moving to a paid League Lab account.
Note: It does cost around $15/yr to register a domain.
One more thing that's important to remember: unlike many websites, you probably care mainly about your local audience. This means the most successful strategies are often the same ones you'd use to promote any local business, including word of mouth, local partnerships, posters, and maybe local advertising like newspaper and radio.