Have you tried this site? Or contacting some of the people who do research all the time?
Dominican Republic Caribbean Gen Web
Picardo is right you need to know Port of entry. I was trying to find something when you first posted. (Yes... I need to get a life.) It seems that all passenger lists from Espana to Las Indias were no longer kept in the archives after 1850. After 1850, the shipping companies maintained lists of passengers. And then the Ports of Entry might or probabbly would have the records. I found that fact on a Cubagenweb site. I suspect it would apply to your ancestor. I would try to find someone who has already done a lot of research into their own family and they can point in the right dirrection. If you want to PM me with your grandfather's name, I could see if I could find something using Ancestry.com. But it's limited in value for immigrants to las Indias, in my opinion.