We went at the end of september 2 years ago. In my opinion the best time to go. It was still warm and we had either no or a minimal wait on the rides.
I just checked and there is the Night of Joy Sept 9-11 at the MK. (Its a lineup of several popular Christian artists.) So either that's cool because you'll get to hear some great music, or not cool because it'll be crowded. Also, if you're planning your trip like the end of Sept into October, the Food and Wine Festival starts at Epcot Oct 1. I've always wanted to see that.