Hello
To obtain the citizenship for a child of a naturalized Dominican citizen, you must follow a process with the Ministry of Interior and Police no with a Dominican consulate. They will required a list of documents and an interview in Spanish, once this process is complete, they will issue a Citizenship certificate and you will be able to apply for his Dominican birth certificate.
The process that is almost automatic are the ones for children of Dominicans parents from birth or origin, not with parents who obtained the citizenship by naturalization.
You can contact Guzmán Ariza law firm for more information.