Do erasers contain carbon

Yes, conventional pencil, pen, and chalkboard erasers all contain carbon as they are made of organic materials.

However at one time there was a typewriter eraser made of a bundle of fiberglass inside a pen like housing, being made of glass (an inorganic material) they contained no carbon. These erasers however generated thousands of tiny airborne particles of glass when they were used, these glass particles could be inhaled causing health hazards and produced intense itching on contact with the skin. For these reasons they are no longer manufactured.