A few folks have explored this. Most recently look at the works of teslaturbo on YouTube. Passive magnetic bearings are quite difficult to perfect, but this work is the closest to fruition. Its important to certain areas of teslas work to reduce friction as far as possible using fluid/air/mag bearings
When I was working Steorm Motor I used passive magnetic bearings it is hard to get balance right. Used part of caliper on each end to help set it up I still have motor in box. I used brass tube to space magnetics on shaft.
I did not find much written on how to balance bearings but did find pictures of build which I made with drill press and table saw. I found an adjustable drill that I could set to any size so I could get a tight fit on holes.
The bottom bolt is used as a stop to keep shaft from going too far. Others used meter at both ends I have 2 but did not want second sticking out bottom. You have to get magnets facing the correct way goal is to have both outer bearings set so they push inner magnets toward the center.
The screw holes in the plexiglass bearing holder where to allow adjustment on bearing spacing.
I used nonmagnetic parts check brass with magnet to make sure they were ok
To adjust I set the bottom stop so when I pushed shaft though the outer bearing it stayed down. Set caliper so it was close to top of shaft then screwed bottom bolt up to press shaft against caliper. Then slowly backed off caliper until and continued to do this until bottom bearing was on the center side of the bearing. Pressure was now on caliper and could then slow move it in or out. Then if did not stay I adjusted screws in plexiglass holder to move bearing to get the spacing that kept shaft centered. This is very close to having the inner and out bearing edges aligned.
It is almost impossible to center by hand using caliper allows you move it slowly and easily repeat settings.
So, if always pops out one side or the other then outer bearings are too close. If one end wobbles than they are two far apart.
Now you could also fix outer bearings and adjust space of inner bearings I just did the away above to avoid taking shaft apart.
Not a good setup in there is vibration is system as it does not take much to pop it out of alignment. With stops it is easy to reset.