  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
intra- and interbilayer plasmon substantially suppresses interbilayer phase
fluctuations, responsible for switching $c$-axis transport from a
superconducting to resistive state. Our calculations indicate that this may
provide a viable mechanism for stabilizing non-equilibrium superconductivity
even above $T_c$, provided a finite pair density survives between the bilayers
out of equilibrium.
