The organisations I have seen in action are mainly secular. They include Plan International, Oxfam (GB and Intermon), Peace Corps, Progressio (formerly known as ICD) Unicef and several others.
They support projects of all sorts in Dominican communities: small business development, micro-credit, farmers groups, crop diversification, marketing, sustainable forest management, youth media, early childhood education and nutrition, health, vocational training, veterinary training, disaster preparedness, community organisation, emergency response.
Some of them also work on the border and in bateyes, which after all are where the most acute poverty is, but most of the work in the DR is with regular Dominican communities.
Provinces include Azua, Barahona, San Juan, several barrios in Santo Domingo, Salcedo, Cotui, Santiago, Mao, Santiago Rodriguez, El Seibo, Miches...
If you're really interested try contacting them directly for specific details or at least check out their websites to see examples of the type of projects, the locations and the beneficiaries.