Summary: Linear stability of the free surface of a thin sheet of a viscous fluid on a vertically vibrated rigid plate, in the presence of a uniform and slow rigid body rotation about the vertical axis, is presented. The Coriolis force delays the onset of parametrically excited surface waves. The creation of Faraday waves is always possible by raising the acceleration amplitude above a critical value, if the angular frequency \(\omega_{\text v}\) of the vertical vibration is much larger than four times the angular velocity \(\omega_{\text r}\) of the rotating plate. The surface waves may be harmonic or superharmonic with the imposed vibration in a thin sheet of slowly rotating viscous fluids at small vibration frequencies. This leads to the possibility of a tri-critical point at the onset of the surface instability in thin layers of a viscous fluid. Subharmonic, harmonic and superharmonic waves with different wavenumbers may coexist at the instability onset in the presence of a small Coriolis force, which is a qualitatively new result.