The only good thing about September in the Caribbean is the cheap price. And the reason it's cheap is for the reasons Brian has given below......Wilba.
September is peak time for hurricanes in the Caribbean so no. Also many ships will still be in Europe and dont go to the Caribbean until second half of October.
As suggested below September is not the best time to go but there are cruises available at that time. There is a strong possibility that the itinerary will change because the cruise lines will not put passengers or ships at risk. October used to be a better month but in more recent years this month has also proved to be, let us say, dodgy. November is much better and from then on is peak time. Lucy X.