So maybe this idea for a semi-workable situation of an otherwise difficult idea. We have a stronger Spain in the 19th century which is especially focused on maintaining what remains of its empire. The Dominican Republic is restored to Spain by Pedro Santana as in OTL, and Spain manages to reach an agreement with it as it later does with Cuba and Puerto Rico to keep the remnants of the Spanish Empire intact in the Caribbean. Into the 20th century, the only independent country in the Caribbean is thus Haiti, which has a somewhat better late 19th century and thus is set up to not be an utter wreck as in OTL. The United States never annexes any Caribbean land.
Decolonisation starts in the 1950s and powerful independence movements emerge throughout the Caribbean. What worked for Puerto Rico, Cuba, and Santo Domingo in the 19th century is no longer acceptable. In the French Caribbean, independence movements are much stronger than OTL, and there's nothing like how Guadeloupe, Martinique, etc. are legally part of France. Likewise in the Dutch Caribbean, and in the Danish Virgin Islands. The independence movements frequently reach out to each other and have many links with each other, and a shared sense of "Caribbean-ness" (compare a "European" identity) emerges due to the historic experience of the peoples of the islands, no matter their race or language. Of course, regional distinctions still exist, especially with the white people of Cuba and the rest of Spanish Caribbean. Within a few years, the Caribbean gains independence in three countries--the West Indies Federation, a French equivalent, the Netherlands Antilles, and a Spanish Caribbean federation consisting of Cuba, Santo Domingo, and Puerto Rico. The Danish Virgin Islands join the West Indies Federation with the permission of Denmark.
These three federations end up working closely together, and eventually federate into a system comparable to the European Union. Haiti joins as well, looking to gain economically. Several years of unusually strong hurricane activity which devastates the Caribbean helps to convince the nations to work more closely together for disaster relief. Although supported by the former colonial nations and the United States, the Caribbean wishes to gain more self-reliance and thus an even more mutual identity is built.
Although many complaints exist in the Caribbean Federation in the 21st century, including but not limited to the dominance of the Greater Antilles in determining many aspects of policy, Haitian immigrants using freedom of movement, and the smaller islands being unduly subsidised by the larger ones, it is hard to imagine the Caribbean Federation not existing with its influence in promoting sustainable tourism and development, protecting the heritage of the islands, strengthening disaster preparedness and relief, and integrating the region to allow it to more efficiently act on the world stage in its own right. It is being proposed more and more that an even tighter union be built between the nations. Supporters of the European Union often use the Caribbean Federation as an example of how to work regional integration. Scenes from the 2010 Haitian earthquake, which killed 30,000 people, captivated the world with their horror, but the soldiers of the Caribbean Federation, a multinational and multiethnic force speaking many languages, assigned to the emergency leading the way in pulling people from the rubble and helping coordinating the rebuilding likewise captivated the world and became iconic images of the tragedy. A later review of the disaster showed that over 200,000 might have been killed without the economic help Haiti gained since joining the Federation, and the timely effort in preventing epidemics was likewise noted.
Certainly an optimistic scenario, but you might be able to lay the groundwork during the colonial era for this to happen. And admittedly, yes, it's the Spanish Caribbean propping up the rest of the Caribbean, although a stronger Haiti and a stronger Jamaica might help, and throw in T&T's oil wealth (and why not the ABC islands too?) for a decent counterbalance to the Spanish islands. Hopefully this will benefit the smaller islands as well.