Baby supplies in Paradise Island, Bahamas

We are travelling with a 7 month old, who for some reason tends to run through an extremely large number of supplies (diapers, wipes, clothes) when he is removed from familiar surroundings. Given the bulk of these supplies, and airline carriage woes, we're seeking possibilities of sourcing there itself.

I am seeking any online resource (with physical store presence), and/or anecdotal experience for the availability of baby supplies. Given the family nature of our hotel, it is likely that they will keep some on hand, but , of course, the pricing may be exorbitant. I am unsure if there are any US-like grocery stores on the island that will stock these as well.