I think I can. From my assessment it appears to be the Lutheran Church, likely Christiansted. Here's why I think so:
1. The first document in the series is a baptismal certificate that bears a stamp from the Lutheran Church.
2. The Lutheran church was the official church at the time (1820's).
3. While most of the registers are simply lists of names, all of the other content is in Danish. The anglican, catholic, and Moravian churches kept their records in English.
4. Several of my family appear in the register, and they were all Lutherans at that time, and all from Christiansted.
Are you local to College Park? I am local and go there with some frequency. I'm going through M1884 now but have a pretty good familiarity with M1883.
By the way, if you have an interest in VI genealogy, you should check out my blog on my research:
http://200inparadise.blogspot.comDave