The Dominican culture is overwhelmingly to give birth in hospitals. I know no one who has used the services of a midwife.
In Santo Domingo, birth preparation courses are popular. There are also special exercises classes for pregnant women offered by certain yoga studios, for instance. Ob + Gyn physicians will refer their patients to these.
I once took Iyengar Yoga classes with a Mexican woman who was here with her husband whose main job was birthing support to women (birth doula). I believe she was married to a large corporation executive and did this on the side. I remember several classes being suspended when she had a patient to support.
She left when her husband was transferred. People paid for her services in cash so the classes and the birth support operated in the informal economy.
Take note that Santo Domingo has a much broader population than Punta Cana. I would not know who her local connections were, as I only took the yoga classes. Just mentioned it so you would know you are not a first to offer birth doula services here.
I would think it would take years for you to get the referrals from the physicians and the patients. Also, wonder what kind of accreditation you would need to operate here.
Bottom line, I would think you would need another profession, savings or source of income to support yourself while you explore using this career in the DR. Even if you offered your services for free you would be trail-blazing in Punta Cana.
Of course you should do your own research, visiting private organisations such as Pro Familia, and then the government public health ministry to see who is offering your services here, and asking and asking around.
From research online there is an organization that gathers midwives in the DR:
https://www.facebook.com/MW4DR
Also check out:
http://doulasdominicana.com
https://www.physiciansforpeace.org/blog/1129
Michaela Arriaza offers doula services turning it into an entrepreneuring experience, would think targeting upscale residents, both Dominican and foreign:
www.baby.com.do