Viscoelastic dampers and belt conveyor systems using viscoelastic dampers to attenuate belt vibration and methods for damping belt speed variations. One version of the viscoelastic dampers includes a low-friction carryway element mounted to a viscoelastic pad that is firmly attached to stationary conveyor framework at various locations along the length and width of the conveyor system. Speed fluctuations of the conveyor belt supported on and advancing along the low-friction carryway elements are damped by the viscoelastic dampers. In some versions, magnetic forces are used to clamp the conveyor belt to the dampers to increase the effective damping.