Carbon is not really a suitable material for a coin. It is either soft, crumbly and black as in graphite and soot, or else it is incredibly hard, transparent and expensive as in diamond.
A few German Notgeld ("emergency money") - or more precisely Notmünze ("emergency coin") - pieces from 1922 are made of "pressed galvanic coal". In the mid-1800s Conrad Conradty established a pencil factory in Rothenbach. By the 20th century, Firm Conradty was making arc lamps and other objects of carbon, including this coin. It measures 34mm in diameter. The inscription obverse is a line from a poem by Goethe, and translates as "Against all forces hold yourself to the defense".
I am not sure exactly what "pressed galvanic coal" is. I don't think this is pure graphite, otherwise it would be much too soft and would not hold its shape. Some kind of binder or matrix is probably used to hold the coin together. As can be seen in the photo, the edges are suceptible to chipping, although the surface is fairly hard. I can not dent it with a fingernail, or even enlarge the edge chips easily (although I didn't try very hard).
500 and 1000 Mark denominations were also made. They are much larger but also quite rare and command prices in the $100-200 range.
I've acquired this beautiful uniface medal made of Pressed Coal, also from Germany. It seems to be some kind of celebration of industrial processes. I hope to learn more later.