Neoprene is DuPontDow's commercial name for polychloroprene.
I'd be surprised if there are any producers of polychloroprene, or even businesses that would hold stock for resale, in DR. Your best bet would be to try contacting polychloroprene producers in either the US or Europe (i.e. DuPontDow and Bayer), and ask them who their representative for DR is.
There are a few chemical import companies in DR that will procure almost any chemical/polymer for you (even in quantities of less than a full-container). Here's a good one: