Here's cobrakiller2000's homemade Levitron-style magnetic top. He says:
The only non-electric way that I know off to get a magnet fully levitating over a magnet and with nice elevation too. Looks way cool and is just overall a beautiful invention in my opinion. Was hard to pull this off. I struggled for weeks before I got it levitating – very delicate system. Yes, gyroscopic forces keep it from tipping over and therefore keeps it in repelling mode as long the rpm are high enough.