Slavery was abolished in 1848 so slaves would have been prior to that. In 1841 and 1846 there were two census forms: free and unfree. If your ancestor was on the "unfree" list then they would be a slave.
Other records exist but are not indexed. Here on Ancestry they have the Slave Tax records that list household and field slaves for each owner. There are a lot and you have to go through them all. Some are impossible to read but many are good.
Additionally, NARA publication M-1883 is devoted to materials specifically on slavery and colored residents, including the 1831-32 register of free blacks, the registers of freed slaves in 1848, and registers of black communicants (appears to be Lutheran).
Beyond that records are incidental. If you find baptismal records they may state race (black, mulatto, mustice, sambo). If they were slaves they indicate owners.
If you are looking for someone in particular, send me the details and I'll see if I have any email@example.com
If you're interested in St Croix genealogy, have a look at my blog:http://200inparadise.blogspot.com