I've been a few times in September. It can rain yes. It can rain lots. But sometimes it doesn't rain. I think my average September day was hot and humid in the morning. About 2pm a storm broke overhead and dumped collosal amounts of water. By 3pm it had stopped and half the crowds had gone home leaving the parks almost empty.
Crowds are lower because the kids are all in theory back at school. It is hurricane season still though.
If it wasn't for the school term thing I would go in September. And bring a poncho.