Just use current designs which, I would think, mechanically constrain the pogo stick except in one direction. Replace spring with powerful magnet (pair), and make sure there's a stop pin or something similar to keep the magnetic pogo stick from disassembling itself.
I think you're making things too difficult and expensive if you're trying to magnetically suspend and stabilize the pogo stick in multiple/all directions.
Also, magnetic radial stabilization would be stable only in a rough sense. The pogo stick handle would still wobble and be disturbingly/unexpectedly unsteady. I think for pogo sticks you'd really want a mechanically confined, piston-like design. You could still have magnetic stops on both extremes.