I tried the non-polar dynamic magnetic levitation. I was successful, using both water and copper to dampen the instabilities.
For safety reasons I used a driving magnet with a center hole so I could slide it on a tool shaft. The cylindrical magnet is magnetized along a diameter (contrary to most magnets) what is what you need in this case. For the levitated magnet I tried both a cylindrical magnet and a cube magnet (both a little larger than the driving magnet).
I used the same rotary tool (Dremel 3000) as on the video above. It has continuous speed control, which is very important as it has to be fine tuned. It's a very cool and interesting effect. Sometimes it attracts, sometimes it repels. Inside the water I could get the magnet to orbit the axis of the tool pretty fast (but much slower than the spinning of the driving magnet). I need to experiment more.