We propose and analyze a scheme for parametrically cooling bilayer cuprates based on the selective driving of a c-axis vibrational mode. The scheme exploits the vibration as a transducer making the Josephson plasma frequencies time dependent. We show how modulation at the difference frequency between the intrabilayer and interbilayer plasmon substantially suppresses interbilayer phase fluctuations, responsible for switching c-axis transport from a superconducting to a resistive state. Our calculations indicate that this may provide a viable mechanism for stabilizing nonequilibrium superconductivity even above Tc, provided a finite pair density survives between the bilayers out of equilibrium.