I need to make this very clear, as I myself am Cuban-American. Cuban-American because I'm the first generation of American-born Cubans. My grandparents came 60 years ago (along with 80% of the middle and upper class of Cuba during the Exodus), my parents were 2 and 3. Now, Cuba's golden age was really in the 1950s, which is the romantic Cuba people still remember. Cuba now is (and I'm not just saying this) a pretty miserable place, since heavy embargos and zip economy have people raising their own animals to survive.
Now, personally, I would suggest the Mambi as their UU. The Mambi was a guerilla fighter that won the Cuban Revolutionary War, and forced Spain out of Cuba. They were basically farmers with machetes that would sneak around in the mountains and slice up Spaniards who were still useing swords and musket-style rifles. Putting them in place of the Knight, giving it a very high attack but low defense and speed, would probably be best.
In addition, you woulden't want to make Castro the leader if you're going for Cuba's "golden age." Bautista (look him up) was the last Cuban president prior to the Revolution/Invasion (depending on who's side you're on).
Cuba was a commercial center, so I would say Commercial and Religious would be the culture traits you want, since it is very Catholic.
NOW... if you're looking for post-commie Cuba, Castro would be the leader you want, and the special unit would probably best be some variation on the cruise missile.
Again, I discourage any use of post-commie Cuba in this because people usually have a very messed up perception of Cuba. That is to say, they see Cuba only after the Soviet-funded invasion of it, not the commercial center it was before. But hey, tiny, remote country. I don't expect people to know this ****.
Anyway, hurry! I wanna play this civ, even if I do have to play as an evil bastard.