September and October are my favorite months to sail. Mostly because the rates are usually the best during that time. Also, it is less crowded than during the summer, but still plenty warm, and the days are still pretty long. The later into the fall that you get, the shorter the days become.
The only caveat is that this is during the height of hurricane season, so there is a slight chance that the ship will be re-routed to avoid a storm. This really doesn't happy very often, maybe two or three times a year. It did happen on one of our cruises, but didn't take away from our enjoyment of the trip at all, and we never encountered rough seas.