"Tree frogs," one of our traveling companions told us. We researched a little and came up with the species Hyla marianae, Jamaican Treefrog. They look like this:
The sound was probably made by male frogs that were trying to attract mates. And although every night we heard them calling, we never could spot them, no matter how still we stood or how hard we looked. To have a listen for yourself, follow this link.