Well, the cedula comes with the residency.
Others will chime in, but I believe a man married to a Dominican woman is entitled to naturalization. I think you have to get residency first [have to live in DR 6 months if I'm not mistaken]. Several threads on this - they have a double standard in DR. As a woman married to a Dominican man, I can go straight for naturalization.
If you click on the Legal Forum [click on the word FORUM at the top left of this page, it will take you to the list of all forums], you can read all the prior threads about this, with links to the government pages that detail the requirements.