Rotating cylinders Halbach array Halbach array - Wikipedia, the free encyclopedia
permanent magnets used as weights on a rotating pendulum and also used as the drive mechanism to change the centre of mass and reduce the amplitude, and also in a conjunction with a belt to push the mass up, increasing the potential energy.
The Magnus effect Magnus effect - Wikipedia, the free encyclopediamay help the parameter change of the oscillator and reduce damping.
Parametric oscillator - Wikipedia, the free encyclopedia
We may use a frictionless magnetic bed for the drive cylinder at bottom and it may work as a storage kinetic energy flywheel, impairing the inwards push of the next weight entering the rotating repulsion magnetic field.
Perpetual motion machine of the third kind?

All the permanent magnetic cylinders are with same polarization. Only repulsion fields are used in all magnetic field interactions.
Picture from Wikipedia.
File:Halbach cylinder.png - Wikipedia, the free encyclopedia

I don´t know what else to add other than the mechanism of swing pumping.
Your opinion will improve it.

Pumping of a Swing - Physics | Grinnell College