Thanks again for lots more interesting leads to follow up. What Margarita was saying about the accent is interesting. Yes, of course black slaves would have learnt their English from English speakers, but this isn't to say that they were "taught" to pronounce the th sound as d. (Parts of Ireland are the only places I can think of, where English speaker do pronounce th as d.) The th sound isn't very common in languages, as far as I understand. If you're learning English as a foreign language, and don't have the th sound already in your repetoire, it can be very difficult to pronounce. I think that's probably how that bit of the black American accent got there.
Cheers,
Jane