Hi Bob
If you mean the spindle itself has play, the rear pulley which holds the belt to the motor is the only adjustment for the spindle, If this is what you mean, put the dead center in the chuck and a piece of wood on that to the tail stock center, apply pressure loosen the screws and tap a couple of times around the pulley to snug it up.
If it's the backing plate itself, let me know.
Hope this helps.