Yes, there are marriage records at the churches. There are some gaps, however. Films are available for the various churches--film for rental is at familysearch.org (select Catalog and put in the place--use VIRGIN ISLANDS (not West Indies). There is film of Dutch Reformed parish registers of St. Croix, Virgin Islands, West Indies: Baptisms and marriages 1764-1814. This may be of interest to you because Frederik was baptised in that church, so you could get his original baptism. Eliza de la Motta was baptized in the Anglican church. (BTW, some catalog info is in Danish, but Google translate helps.) Have you checked the extensive genealogy for Billenstein at www.vifamilies.org? Each piece of info is well documented to take you right to the original source. I see also that Billenstein was born in Copenhagen, and you may find some very interesting info when you go through the Danish census, which is online. You have to search it by counties, but with a little patience, you may be glad you did.

Happy hunting,
Laura