They possibly date from the warehouses that were there before the towers. maybe there was a Jamaican social club or a shrine to Santa Money for Jamicans or something.
The coins would predate the buildings as Jamaica went decimal before 1970. What era are the halfpennies as they were made from the 1860s onwards.
UPDATE - seems they were stored in some vault 2 stories underground by Comex (For what I don't know) and several scammo home shopping companies are selling them for $100 or so each when in reality they are worth cents. It seems the 9/11 provenance of them has made them valuable.
The coins are also very late (1950 - 1969)
Another dumb TV coins scam that rips at sentimental heartstrings (9/11), how a Jamaican coin would appeal to that is beyond me.