There’s no traditional wedding gifts really. Colorful, Dominican street art on canvas can be found everywhere (they are actually copies of famous Haitian art).
You also can find some primitive stone Taino god statues in many of the gift stores. Here’s a link showing some masks and Taino figurines http://www.tainogallery.com/symbology/ http://www.tainogallery.com/gallery/masks/ Do a google images search for “Atabey” (goddess of fertility).
For an idea of Dominican/Taino pottery… http://dominicancreations.com/SHOP/xcart/Taino-Aboriginal-Sculptures-Amulets/
Haitian metal art – hand punched designs made from steel oil drums http://www.haitimetalart.com/Haitian_Metal_Art.html Easy to find on the north coast but not sure if you’ll find quite as many designs on offer in Punta Cana.
Traditional faceless dolls dressed in brightly colored dresses, made from red clay.
Lots of wooden carvings and bowls (make sure they don’t have dreaded woodworm!).
Gift shops are everywhere. A couple of nice ones in Palma Real Shopping Village 20 minute cab ride away (check with your hotel concierge for PRSV shuttle times)
If the bride is into cooking there’s this excellent Dominican cook book, I use it myself and it’s the best one I’ve seen http://www.amazon.com/Traditional-Dominican-Cookery-Clara-Gonzalez/dp/9945045016
And, of course there is Mamajuana – the rum based aphrodisiac
Good luck shopping!