Jefmaka,
While I am not paying any potential loss, I also have been involved in the property and auto insurance industry since 1980 (which is an odd coincidence) and am familiar with the auto insurance contracts in Jamaica. Without being added as a named insured on your friend's insurance policy, you would not be covered as a tourist in Jamaica to drive the car. The fact you gave them money for the car and they are letting you borrow it is an obvious barter arrangement and would not be covered under the standard insurance contract.
I have seen this happen more times than I wish I would have, and even while everyone is well-meaning, that does not make the insurance coverage extend to good intentions. Craig123's advice is wise - you will need to contact the insurance carrier/broker and be completely above board and forthcoming with the true and accurate representation of the facts in the matter. Any misrepresentation or falsehood made would make the insurance coverage null and void.
