We've gone quite often in October, my hubby's birthday is the 20th. We've had very few days of rain. Usually, when we have hit rain, it will rain for about 20-30 minutes, then the sun comes back out. July and August are pretty steamy months, it's the dog days of summer. Hot and humid, but great for swimming/snorkeling/diving. September and October are usually nice.
You do run a chance of a hurricane, but if that does happen, they will reroute the ship.