The Aruban low season is usually the cheapest time to fly from the United States of America to Aruba. The low season is from the middle of April to the middle of December. Basically Aruba has year round pleasant weather. Its high and low seasons refer to climates in the U.S. and Canada. When its winter in the U.S., Arubas sunny, warm climate beckons. Thats the high season: the middle of December to themiddle of April.
I think that the best way to find the cheapest flights is to sign up at one of the websites specialized in airfare deals alerts. However I think you can buy the cheapest tickets for fall - but it also depends when you buy them..