The challenge is one of two scenarios: A British or American Cuba (As a state) with a majority English-speaking, American/British-origin population. If British, then still majority English-speaking and culturally more British than Hispanic, similar to New Zealand or Australia. If American, then as a state and majority English-speaking and populated by people coming from the United States mainland, and culturally as "American" as any mainland state is. It would be as free and prosperous, and peaceful as any other constituent territory of the United Kingdom or United States is today.
Would the War of Jenkin's Ear accomplish this?
And, what's the most plausible chain of events? What's the earliest PoD for either American or British Cuba that doesn't alter the US appreciably?