Your challenge is to find a way to have the Kingdom of Spain take Jamaica and/or the Bahamas from the British with a POD after 1783, and hold onto it for as long as possible. It can gain independence but cannot be taken back by Britain.
Well the Spanish traded the Bahamas back to Britain in exchange for East Florida at the end of the ARW. East Florida was a very unhealthy station for the British garrison and it had been reduced to under 100 effectives in St. Augustine. It really wouldn't have taken much for the Spanish to sail in and take the place outright.
Jamaica is harder unless the Spanish take Gibraltar which to say the least would be difficult though not impossible. There are two options.
1) The British relief fleet that was sailing to Gibraltar was blown past the base by a storm. The Spanish Admiral made a mistake in pursuing the fleet rather than sailing directly to Gibraltar and positioning himself between the British fleet and Gibraltar. This of course doesn't guarantee a Spanish victory just a bloody battle that the Spanish may win.
2) After the British fleet successfully resupplied Gibraltar the British attacked the Franco-Spanish army's siege lines. The attack was successful but suppose the Allies are ready and planted a large mine that destroys the attacking force and opens the door for a counterattack.
Of course you are also going to have to take Jamaica itself which is actually probably the hardest element of this challenge.