I could imagine that they were in natural Wood, possibly lightly tarred. If they were painted in any colour this would have been widely publicised by now. I believe the 1:10 scale model in the museum also has the carriages in natural wood.
Sorry not to have answered this earlier (although it is a question I have answered several times on this forum and others). Purchase records for the navy yard indicate that they bought lamp black specifically for painting gun carriages, so the carriages should be black.