Ron,
In the past the off peak season was considered to be May through November, but tourism has increased a lot the last five years. Certainly, July through October tourism is much slower than December through April. But Ambergris Caye is busier during the summer than in the past. But many hotels and resorts offer lower rates in the summer, June through November, and deals can be found on line. Check the hotels’ websites for their posted rates, which usually show the seasonal differences.
From what I’ve heard, Placencia is still quite slow in the summer, as is the Cayo. I’ve noticed that many tourists on a tight budget tend to come in October. October seems to have the lowest rates, but it is also the height of hurricane and rainy season. Sometimes it rains for days on end. Other times the weather is delightful. It’s just riskier than the early part of the year, which is when the weather is perfect and the rates high.