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We propose and analyze a scheme for parametrically cooling bilayer cupratesbased on the selective driving of a $c$-axis vibrational mode. The schemeexploits the vibration as a transducer making the Josephson plasma frequenciestime-dependent. We show how modulation at the difference frequency between theintra- and interbilayer plasmon substantially suppresses interbilayer phasefluctuations, responsible for switching $c$-axis transport from asuperconducting to resistive state. Our calculations indicate that this mayprovide a viable mechanism for stabilizing non-equilibrium superconductivityeven above $T_c$, provided a finite pair density survives between the bilayersout of equilibrium.

Proposed parametric cooling of bilayer cuprate superconductors by terahertz excitation