If I had to find the damping constant of a material then I would look for FMR measurements of that material, since the FMR linewidth depends linearly on the damping constant. Or you could try to find out what other people have used when simulating the same material.
If you do Monte Carlo simulations then you don't have to worry about the damping constant. For dynamical simulations of Tc you should set critical damping, alpha=1.0, to try to compensate for the speed of the temperature sweep (0 to 1000 K in 1 ns or less). Lower damping will make it seem like the Tc is higher than it actually is, just because the spins didn't have time to relax.