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Well, the answer to this question - at least from the perspective of the context with which I'm most familiar, which is the British Caribbean - is a little complex and involves getting into a lot of regional political history, so brace yourself for a long answer! It's also a little late here, so please excuse any minor oversights in editing.

It's worth pointing out first and foremost that the Caribbean is an extremely broad and diverse region. In its broadest sense, the Caribbean incorporates the West Indies - a region that consists of more than thirty distinct entities (most of which have meaningful self-government) - as well as Belize, Suirname, the Guianas and parts of Venezuela and Mexico. The Caribbean basin region includes many more countries on the mainland. There are half a dozen major languages in the Caribbean sea region and the region as a whole is characterised by not insignificant ethnic diversity. More than half of the entities within the Caribbean islands are still possessions of nations in Europe or the United States, including several places that are popularly misconstrued to be fully independent countries - like Bermuda (a territory of Britain), Aruba (the Netherlands) and Puerto Rico (the United States). Although Caribbean island countries especially are often treated with a kind of casual dismissal by those of us from larger countries, each island in fact has a rich and complex history, and the politics of most Caribbean states are thoroughly modern, complicated and utterly fascinating. Within that context then, efforts to unify the entire Caribbean would certainly be incredibly complex and difficult task.

Within the British Caribbean though, there have been historic efforts to create political entities or states that include multiple modern-day Caribbean countries. In particular, the islands of the British Caribbean have a long history of federal governance. From 1671 to 1871, with the exception of the period 1816 - 1833, the islands of Antigua, Barbuda, Saint Kitts, Nevis, Anguilla, Dominica and Tortola (as well as various smaller islands) were governed as a single colony with a central government. From 1871 to 1956, several of these islands formed the Leeward Islands Federation as a colonial possession of Britain. Similar, though rather more haphazard, arrangements existed throughout the region at varying points - for a time in the 19th century for example, Grenada and the Grenadines, St. Lucia, St. Vincent, Tobago and Barbados also formed a single colony known as the Windward Islands. Centralising government within a federal structure was a British tactic for making the cooperation of the region's development more effective and, from the early 19th century onwards, enhancing the power of the Colonial Office.

These were not truly unified countries like the kind you describe, though. There was no semblance of a union of equals - Antigua had primacy within the Leewards, and Barbados within the Windwards, although Barbados' relationship as part of the Windward grouping was complex. Individual islands remained largely self-governing despite the existence of central structures; there was no federal legislative body in either island grouping, with elected legislatures being based on individual islands (though these legislatures were eventually abolished over the course of the 19th century). Central governors were aided by deputies for each colony who often administered affairs as de facto governors in their own right, particularly in the Windward islands, the central power structure for which was critically undermined with the withdrawal of Barbados from the union in 1885. These were also flexible structures, as noted by the disruption of the Leeward Federation briefly from 1816 - 1833 when it broke into two smaller federations, and by the movement of Dominica from the Leewards to the Windwards in 1940.

By the beginning of the 20th century, the authority of the imperial government in the British Caribbean was in decline. The centralisation of power that had occurred through the 19th century after the abolition of slavery began to be reversed, with the re-establishment of local legislative bodies and increasing autonomy for individual colonies, though access to political power was severely restricted to exclude the non-white majority in society from meaningful representation and influence. The 1930s proved to be a pivotal turning point in Caribbean history, and set most of Britain's colonies on the path to independence. The onset of the Great Depression in 1929 had exposed catastrophic economic mismanagement on the part of the colonial governments of the region: being so completely dependent upon agricultural exports to the United States and Europe, the subsequent collapse in demand for these goods facilitated by the global economic crisis triggered dramatic increases in unemployment and poverty across the islands.

Beginning in late 1933, a series of violent riots and general strikes broke out across most of Britain's possessions in the region, driven chiefly by African Caribbean anger at appalling economic conditions and the inability - and unwillingness - of white governments to address them. The unrest persisted intermittently but relentlessly for four years, and initial attempts at repression only served to make matters worse. It was in the context of these riots that clear national political leaders emerged in opposition to British rule - men like Alexander Bustamante in Jamaica and Grantley Adams in Barbados. The first meaningful trade unions also began to organise successfully and on a mass scale, often around these personalities, creating organised vehicles for political change, many of which would later become political parties. It should be emphasised that this was certainly not a sudden political awakening on the part of the Caribbean working class - far from it. The history of the Caribbean shows us that throughout for centuries, black, Asian and white working class people alike were very much willing to assert demands for political and social change whenever they felt able. Rather, particularly for those descended from African slaves, the 1930s labour riots represent a significant shift in the political landscape of the Caribbean because they led to the emergence of real, sustainable vehicles of political change even after the unrest had died out. Likewise, decades of limited social mobility had produced a middle class of black and especially mixed raced men and women who were prepared and able to take up the task of organising resistance to colonial rule on a national scale.

These were not revolutionary movements emerging in this period; though the idea of independence began to be raised in the 1930s, by and large the emerging labour movement was interested in forcing the British authorities to widen access to existing political power structures and do more to tackle poverty. These were struggles for autonomy rather than independence, though independence would grow in significance as a goal consistently thereafter. The British government commissioned a report into conditions in the Caribbean that reported behind closed doors in 1939, though its conclusions were kept secret until 1945 to avoid it being used as anti-British propaganda; that report found conditions in the colonies woefully inadequate and called for dramatic improvements in service provision, but struggled to find workable solutions (one of its more retrospectively ludicrous recommendations was that women should quit their jobs to help boost male employment, and women could then fulfil the role of social service provider).

An experiment with self-government began in Jamaica with the holding of the first free, fair and universal democratic elections to a new colonial legislature in 1944. The results of that poll were a stunning blow to the local elite; despite an extremely well funded and organised campaign to elect white planters and sympathetic, affluent black merchants to the legislature to represent the interests of the establishment, all 32 seats in the new chamber were won by opposition parties, and the Jamaica Labour Party - an organisation that was essentially just a political platform for Alexander Bustamante, the mixed race lawyer who had emerged as the figurehead of the 1930s unrest - secured enough seats to govern alone. Two years later, despite the absence of the same kind of open and free processes, the Barbados Labour Party secured a similar election victory. The political structure of the islands was rapidly beginning to fall apart and fragment, with British authority and the authority of local elites alike in sharp retreat in the face of increasing non-white resistance to colonial rule.