  The photoproduction of isolated photons has been measured in diffractive
events recorded by the ZEUS detector at HERA. Cross sections are evaluated in
the photon transverse-energy and pseudorapidity ranges $5 < E_T < 15$ GeV and
$-0.7 < \eta < 0.9,$ inclusively and also with a jet with transverse energy and
pseudorapidity in the ranges $4 < E_{jet} < 35$ GeV and $-1.5 < \eta_{jet} <
1.8,$ using a total integrated electron-proton luminosity of 456 pb$^{-1}$. A
number of kinematic variables were studied and compared to predictions from the
Rapgap Monte Carlo model. An excess of data is observed above the Rapgap
predictions for $z^{meas}_{Pomeron} > 0.9,$ where $z^{meas}_{Pomeron}$ is the
fraction of the longitudinal momentum of the colourless "Pomeron" exchange that
is transferred to the photon-jet final state, giving evidence for direct
Pomeron interactions.
