earlier bedwood was black, the particular type of finish material varied, or isn't well documented - by the TF years the bed floors were being painted body color
if the paint is peeling Cape, there's no way to 'stick' it back, the loose stuff will need to be scraped off, so you're looking at repainting, or if that doesn't leave it looking too patchy, at least scuffing the whole thing and clear coating
Bill