Many records in areas that were occupied near the onset of the Civil War seem to lack surviving cohabitation records.

However, a couple of sources exist to get at the information indirectly via birth records. Virginia recorded births of slaves and FPOC @ 1853/1855 (at least I've found some in Norfolk at the local and state level). I've found evidence of "mixed" marriages, where the mother was free and the father identified by name as a slave. But these examples are probably less than a dozen.

Beyond that of course, there are pension records. And then some churches formed in the antebellum period have records. I've yet to find a consistent source.