This is along the lines of what I was thinking initially but more by reacting to the instantaneous current induced in the coil rather than a charge/discharge action.
Where the ring launcher works by counter emf that evolves in the conductor, a tuned emf (like for RFID chips) could be made with specific properties. Eg. it might only respond to certain frequency bands and possibly (?) allow for both repulsive and attractive forces by either maintaining or inverting the exciter phase in the board.
You could let a microcontroller on the puck control the allowed currents. If you do this sufficiently fast, you can multiplex over different pucks on the board.
Creating a tuned oscillator could be interesting too, but could also turn out to be too heavy, in terms of component weight.
Basically a small version of the ring launcher - https://www.youtube.com/watch?v=V690VphqTwg
Where the ring launcher works by counter emf that evolves in the conductor, a tuned emf (like for RFID chips) could be made with specific properties. Eg. it might only respond to certain frequency bands and possibly (?) allow for both repulsive and attractive forces by either maintaining or inverting the exciter phase in the board.