  Standard optomechanical cooling methods ideally require weak coupling and
cavity damping rates which enable the motional sidebands to be well resolved.
If the coupling is too large then sideband-resolved cooling is unstable or the
rotating wave approximation can become invalid. In this work we describe a
protocol to cool a mechanical resonator coupled to a driven optical mode in an
optomechanical cavity, which is also coupled to an optical mode in another
auxiliary optical cavity, and both the cavities are frequency-modulated. We
show that by modulating the amplitude of the drive as well, one can execute a
type of STIRAP transfer of occupation from the mechanical mode to the lossy
auxiliary optical mode which results in cooling of the mechanical mode. We show
how this protocol can outperform normal optomechanical sideband cooling in
various regimes such as the strong coupling and the unresolved sideband limit.
