You've hit the nail right on the head.....it's about creating an atmosphere of FUN.
Organizing leagues is not fun, but creating a social atrmosphere with great music (no juke boxes), and special, VIP treatment for ladies. Ladies want to be treated special, that's the only secret, that means discounts or complimentary pool, drinks, food, valet, etc.
I had a nightclub in North Dallas that had 630,000 Members, MANY of which were female and we catered to them specifically. We had free cover, free pool, discounted "female friendly" food items, free valet, and SECURITY that made sure they were treated with respect and courtesy.
With this formula we were #1 in the state of Texas in liquor sales 2 years in a row (we beat all bars, restaurants and billiard clubs, and behind two strip clubs for obvious reasons

)
There's many ways to cater to women at whatever level you choose, just remember the most important things are safety, cleanliness,clientele, and pricing structure. If someone talks disrespectfully to the female clientele or staff members, it's best to eliminate them immediately for the night or forever, this is a judgement call.
Women really like to see they are protected and it sets the "sample example" in an appropriate manner and will sort out the undesirables in the process.