I find it hard to imagine someone doing an authentic Afrocarib accent without growing up around it, simply because they are so difficult (Mainly speaking about Jamaica here, but some of the other islanders sound similar so the logic may still apply), but that can depend on how rough it is. The sentence structure is also switched up.
Whereas an American may say "It's not a thing you know."
A Jamaican will say "Is not a t'ing enuh." (I use an apostrophe because they often leave out the 'h' in 'thing'.) They also use "say" a lot before they are about to explain something, pronounced as "seh." They also often replace the plural s by saying "them" (pronounced dem) to signify they are talking about several of the same thing.
American: "You know the chickens are gone?"
Jamaican: "You know seh de chicken dem gone?"
As far as I can tell, other more popular accents still keep the same sentence structure that we're all using right now, but that's just my 2 cents.