I am thinking of using a short cylinder as the shape of the chess piece, but then I can't figure out how to make one side of it to be black and the other side to be white.
I want to do it this way as I want to have the pieces flipped during the game, just like we play Othello in the real world.
Edit: In addition to Nigel's suggestion, a "thin" sphere with a "black/white" texture applied to it can also get the job done.
You can use 2 cylinders ("black" and "white") properly ("black" is standing on "white" head) grouped under one parent object. Then:
this.renderer.material.color = Color.black;