Hurricane season is officially June 1 to November 30.
August/September is usually considered peak activity time. But you could go and not have any hurricanes or tropical depressions during that time. It is the rainy season so be prepared for some rain most days. It usually only lasts for a short time every day, maybe an hour or so. But it can last for a few days. No way to know.
High season in that area is December, January, February, March. Warm weather and very little chance of rain.