Q:

Passive spin damping system

I'm thinking of how a satellite can be fully passively stabilized.
We have two passive attractors, forces that draw the satellite towards a certain orientation. A bar magnet will orient along the magnetic field axis, and a mass on extended arm will orient the craft along the gravity gradient.
These two are sufficient to establish a fixed (or at least known) "preferred orientation" relative to Earth, but they are insufficient to stabilize the craft due to nearly nonexistent friction to extinguish oscillations around the preferred orientation. Besides the attractors, we need dampers to create friction-like forces.
For magnetic field, there's a permalloy bar with a hysteresis of magnetic field orientation. In changing magnetic field, it will act like friction, opposing the rotation and dissipating the kinetic energy through eddy currents. But again, it acts along the magnetic field axis only. We still have an oscillation around the axis - in the plane passing through gravity gradient axis.
How can we dampen this motion?

A:

A rotational viscous damper is what you're looking for, commonly called a rotational dashpot.  Normally on Earth these would dampen between a fixed ground system and the moving system, in space it would be designed to dampen between the moving satellite and the fluid itself in the damper.
Most basically it is a cylinder of fluid whose inertia is going to resist rotation.
https://en.wikipedia.org/wiki/Attitude_control#Pure_passive_attitude_control
For mass saving you could design your fuel tanks for an active thruster system to act as the passive damper.

