OK, I'll bite.
Pre-WW1: In the late 19th century, there had been proposals for Jamaica (which, up until OTL Jamaican independence, contained the Cayman Islands and the Turks and Caicos Islands as dependent parts of the colony) and Barbados to join Confederation. To satisfy the "post-1900" name of this board, let's say that those two are successful before 1914. That's 5 OTL Caribbean countries taken care of.
Interwar: At the Paris Peace Conference (and for some time beforehand), Canada becomes insistent on handing the BWI over to Canada, most likely as LoN Mandates. Eventually, Lloyd George agrees, but Bermuda is adamant in their refusal to join Canada; in Newfoundland's case, they are already independent and prefer to be that way - due to the pre-WW1 POD, the disaster that was Beaumont Hamel is largely avoided, so at the end of WW1 most of those Newfoundlanders who served at the Front survived. A larger population in TTL, which would be seen as a miracle, means that much of post-WW1 Newfoundland history, such as the Commission of Government and its history as part of Canada, is butterflied out of existence. As such, nobody in Newfoundland wants to be part of Canada, even with Newfoundland's economic dependence on the rest of North America. For the most part, though, those two are outliers.
From here, two paths can be chosen. The first path is the most obvious, which ignores the butterfly effect - i.e., WW2 still happens as in OTL. Another path would be France electing the Action Française (or similar groups) to power, which could partially butterfly away WW2.
Path No.#1: No Free French arising due to the butterfly effect means that once Vichy France is created, Canada begins fighting for France's Caribbean territories. Once gained, they are put under effective Canadian occupation for the rest of the war. The same also holds for Newfoundland vis-à-vis Saint-Pierre et Miquelon (literally in this case, as the archipelago is just a stone's throw). As it turned out, however, Canada's occupation of the French Caribbean was such a refreshing (and liberating) change that after WW2, much of the French Caribbean clamor to join Canada. Under this proposal, Guadeloupe, Martinique, and French Guiana become separate provinces, but Guadeloupe also has Saint-Martin and St. Barth as dependencies (similar arrangement as per Jamaica; in OTL this was also the case as well for the French Overseas Region of Guadeloupe, however since 2008 - IIRC - those three are now separate French overseas regions). The liberated French are forced to agree. Saint-Pierre et Miquelon, however, chooses to remain part of France.
From there, things get more interesting. Between the 1930s and 1950s, Canada's LoN Mandates make petitions to become part of Canada, which Canada obliges (with the consent of the UK and the LoN). As before, though, Newfoundland and Bermuda remain outside of Canada's orbit - Newfoundland as an independent Dominion, and Bermuda as a Crown Colony of the UK. However, in the 1960s, protests and violence erupts between the various communities in Bermuda. One of the demands amongst the disadvantaged Black community is to have Bermuda part of Canada (marking a shift from pre-WW1, when it was White people having Jamaica and Barbados part of Canada), which eventually becomes the case. This leaves Newfoundland and Saint-Pierre as the lone holdouts.
In the case of Newfoundland, there's good reason to keep independent - the prospects of oil being found nearby leads to explorations during the 1950s into the 1970s (though some work began in WW2 in TTL), with production commencing during the 1970's. By then, Saint-Pierre had been making noises for some time to join Newfoundland - usually, though, those noises fell on deaf ears in France. During the 1970's, though, Saint-Pierre goes crazy about it, so France was forced to work on that; it was not, however, until 1984 that Saint-Pierre became part of Newfoundland - even then, Saint-Pierre retained a special status within the Dominion. (By this point, Newfoundland and Canada are essentially the only countries in the Commonwealth which maintain the use of "Dominion" in its name and in everyday usage.)
During the early 21st-century financial crisis, though, even Newfoundland wasn't immune - indeed, things became so bad that (more due to political manipulation on both sides than anything else) Newfoundland eventually became the last province to join Canada. Not surprisingly, Newfoundlanders are not happy with this, and in TTL, there is currently a major movement in Newfoundland to secede from Canada and become its own country again.
Path No.#2 I'll elaborate on later.
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@stewicide: Canada wanted the BWI at the Paris Peace Conference for one simple reason. To sum it up - why should Australia have much of the UK's and defeated Germany's stuff in the Pacific and we are left with absolutely nothing similar, even though we are the oldest Dominion? In other words, using the precedent of Australia to try to force Britain to hand over all her Caribbean colonies to Canada. At this point, I should make a point that, despite popular belief, Bermuda and the Bahamas are not considered to be part of the Caribbean - especially in Bermuda's case, when they are in the middle of the North Atlantic.
However, one should not discount pre-WW1 proposals from some of them, particularly - as I've noted in my little scenario - Jamaica and Barbados, both of whom were very serious (at the time, which here means the mid-to-late 19th century) about joining Confederation. In both cases, both Ottawa and Whitehall dropped the ball. If, on the other hand, both Jamaica's and Barbados' bid was successful, it would not be unreasonable to have more follow.