roatan island, belize and cozumel.
For Roatan there is Fin's and Flipper's resort which is very close to where the ship docks.
I would not take a 9 month old in the Belize water taxi...first of all they do go very fast and hit the waves very hard once they hit cruising speed. Some have enclosed passenger areas, others are wide open. We've lost hats, sunglasses and other stuff have gone flying out of the boat due to the high speed and rough ride. The other reason is that to get to the water taxi you have to leave the security of the Belize tourism village and walk down a street to where you buy your ticket. We have done this a few times ourselves, but it was only because we had a very large group and some very big intimidating looking men escorting us. We had no problems but I just wuldn't be comfortable doing it with a baby.
I woul recommend the ship's tour (I can't recall what it's called) but it takes you over to Spanish Bay on a tender. It's close by and its one of the few places in Belize that has a beach. They have floats and stuff. There is a restaurant on the other side of the Island owned by Hugh Parkey's Divers. You will feel safe and no one will bother you there. We thought it was fine for a day with the kids.
In Cozumel, I would recommend getting a rental car through Ace/Executive car rental (reserve it in advance) and rent a car seat if you aren't bringing your own and go to one of the beautiful beaches along the main road that circles the island. It is very easy to get around Coz.