We always go at that time of year. Weather isn't quite as hot and humid as July, but still pretty much so. Rain, if you have any, is usually there and gone before you know it. Last September we only had one afternoon shower the whole week, and we were taking our afternoon nap at the resort when it hit. The only thing is, September is still hurricane season - in Sept. 2001 we were there during a tropical storm, which hit the day after 9/11. Miserable trip all the way around.
Accuweather.com is the site we like since it gives 15 day forecasts, and can help with planning what to take.