The ZEUS detector at HERA has been used to measure the photoproduction of isolated photons in diffractive events. Cross sections are evaluated in the photon transverse-energy and pseudo-rapidity ranges $5-15$ GeV and $-0.7 - 0.9$, inclusively and with a jet of transverse energy and pseudo-rapidity in the ranges $4 - 35$ GeV and $-1.5 - 1.8$, for a total integrated luminosity of 456 pb$^{-1}$. Further kinematic variables studied include the fractions of the incoming photon energy and of the colourless exchange (``Pomeron'') energy that are imparted to a photon-jet final state. Comparison is made to predictions from the RAPGAP Monte Carlo simulation.