I'm no Civil War expert by any stretch of the imagination, but I have had several occasions to do some reading about this particular subject.
I got hired by the Monitor Marine Sanctuary and the Mariners' Museum some years ago to design a paper model of her, for use in those organizations' education programs. In the course of that project I dug through all the published sources I could find and picked the brains of the folks who had been diving on the wreck of the ship. The consensus seemed to be that the Monitor had an extremely simple color scheme: black above the waterline and red oxide below. The red used for that purpose in those days seems to have been a considerably brighter shade than what we normally associate with bottom paint nowadays - a slightly orange-ish shade. The experts seem to think her iron plating was painted black. Not the most interesting or challenging of color schemes.
Scarcely any really reliable information about the Virginia's appearance seems to exist. I imagine it's possible that the original Merrimac was copper-sheathed below the waterline; that seems to have been standard practice in the U.S. Navy of the era. Most well-executed models of her, though, seem to show her in a scheme similar to the Monitor's, with red-lead paint below the waterline.
Last year my students and I worked on a project in association with one of the few surviving (well, sort of surviving) Confederate ironclads, the C.S.S. Neuse. She was burned to prevent capture by the Yankees, and sank in the Neuse River near Kinston, North Carolina. The remains of the hull are on public exhibition. I had some lengthy discussions with the guys at the state historic site where she's exhibited; they know far more about this stuff than I do. Their opinion is that Confederate ironclads were "painted" overall with a concoction that the Confederacy (and, I suppose, probably the Union too) used as a protective coating for all sorts of metal - notably cannon barrels. It was a mixture of black paint, tar, turpentine, and maybe some other substances; if it wasn't pure black it was pretty close to it. (Maybe a sort of brownish-black.) The folks at the Confederate Naval Museum, in Columbus, Georgia, seem to be of the same opinion. I must say, though, that some of the photos of Confederate ironclads on the Mississippi seem to show a lighter color - probably grey.
Whether the Virginia (the first of the type, fitted out before any precedent or standard had been set) was painted that way is hard to say. It's occurred to me to wonder whether, given the circumstances of her "conversion," she was painted at all. It's certainly conceivable to me that the planking on her decks might have been left natural.
Maybe some Civil War enthusiasts in the Forum can help out more than I can with this one. But I'm inclined to think the black and red scheme is right for the Monitor, and that the Virginia leaves plenty of scope for personal interpretation.