This Used To Be My Playground Don't know the history of the league but it was during WWII when men were overseas a woman's baseball league was formed. A fictionalized and cute movie this was set during the time period/league.
The film revolved around two sisters and their drama, one (Geena Davis) the more talented and athletic one but the other sister more determined. But many good supporting players in this one: Tom Hanks as the washed up major leaguer now drunk manager, Madonna as the deviant dancer, Rosie O'Donnell as the loud mouthed infielder, Bitty Schram (Monk's assistant!!) as the meek outfielder, and her son as the bratty kid. The supporting cast made the movie imo.
There's No Crying in Baseball still gets quoted till this day but it's always that line This Used To Be My Playground and song that stays with me. Nostalgia there.