Meredith and David Lamb have experimented extensively with techniques for levitating graphite. I learned from Meredith's web site how to achieve stable levitation of a thin rod of graphite (The box labels for the rods indicate: "National Special Spectroscopic Electrodes. Highest purity product obtainable. National Carbon Company. Division of Union Carbide Corporation.") that I Meredith gave me. Starting with a 1/8-inch diameter rod, I sanded down a 1 3/8-inch-long piece to a half-moon shape.
Top View

End View (dime in foreground for scale)
The magnets were purchased from Forcefield/Wondermagnet. They are gold-plated, 1-inch long by 1/4-inch diameter. Each rod is magnetized with the north pole along one edge of the rod and the south pole along the other - NOT with the poles at each end of the rod. I started with 4 such magnets and two of them broke when they snapped down onto an iron surface.
The magnets above are held against a metal shelf bracket. I found that without an iron backing the graphite would not levitate.
Click here for a 1.2 MB MPEG video of the graphite oscillating back and forth.
4/15/01
I discovered why it was necessary to have the magnets held against a metal backing. I drew lines from the north to the south pole a the end of two magnets. When the magnets are not against a metal plate the lines representing N-S:N-S form one straight line. When held against an iron surface the poles rotate to form a 90 degree angle. The photo below shows an end view of these lines:

Magnets with lines showing location of magnetic poles, and V-shaped graphite
containing a slip of white paper.

Top view of magnets, V-shaped graphite, and penny for scale.
Click here for 0.8 MB mpeg video of oscillations.