bar-b-barn(not A/I) worked out good when my child was that age
it's directly on the beach
has 2 restaurants with more in walking distance
ask them for room 118 (my room) - it is close to the bar and i felt comfortable putting my child down for a nap or to bed because i could see the door from the bar (able to eat food at the bar)
as he got older - he could go get breakfast and i could hear him interacting with the staff from the room
take plenty of action figures - i found they worked real well after the sand castle is built - the action figures would keep my child occupied for hours and would attract playmates for him

have fun! jamaica is very child friendly - i never realized how much until i started going with a child - it was a whole new experience

i also arranged babysitting for a very minimal charge and my child LOVED his sitter