I can't be certain what was originally used, but you should be able to
get black French polish from a specialist supplier.  It is certainly
available in the UK, I have some.  This will, of course, give a gloss
finish.  For a matte finish I have used blackboard paint.  The one made
by Rustin's in UK smells like French polish, so is probably similar to
that originally used.

I have an old book on wood finishes which suggests that the colour is
actually from lampblack, which you can produce by holding a piece of
bright tinned plate over a smoky gas flame, but it will take a while
to accumulate a decent quantity.  Then dissolve this in white French
polish.  (The book also suggests adding something called "Reckitt's
Blue" to intensify the colour, but I'm not sure whether that exists
in the US, or even in the UK; it was used to intensify the whiteness
of washed clothes.)  Otherwise you can use black spirit aniline dye:
the book says 1/2 ounce of dye to 1 pint white polish.

John Farmer, UK
(Archivist, MBSGB)