  We introduce Gilmore-Perelomov coherent states for non-unitary
representations of non-compact groups, and discuss the main similarities and
differences with respect to ordinary unitary Gilmore-Perelomov coherent states.
The example of coherent states for the non-unitary finite dimensional
representations of $SU(1,1)$ is considered and they are used to describe the
propagation of light in coupled PT-symmetric optical devices.
