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Yes, slave birth certificates are notoriously difficult to find. The Nationaal Archief of the Netherlands has a guide that might be of help: "I'm looking for an ancestor who was a slave in Suriname."
The link within this guide to the Nationaal Archief in Suriname is broken, so here is a corrected link. Note that the site is only in Dutch - no English. You can search their catalog here: Archievenoverzicht (Archives Overview). Some of these collections date back to the time period you are looking for.
I wish you the best of luck in your research!