  Diffractive photoproduction of D*+/-(2010) mesons was measured with the ZEUS
detector at the ep collider HERA, using an integrated luminosity of 78.6
pb^{-1}. The D* mesons were reconstructed in the kinematic range: transverse
momentum p_T(D*) > 1.9 GeV and pseudorapidity |eta(D*)| < 1.6, using the decay
D*+ -> D0 pi+_s followed by D0 -> K- pi+ (+c.c.). Diffractive events were
identified by a large gap in pseudorapidity between the produced hadronic state
and the outgoing proton. Cross sections are reported for photon-proton
centre-of-mass energies in the range 130 < W < 300 GeV and for photon
virtualities Q^2 < 1 GeV^2, in two ranges of the Pomeron fractional momentum
x_pom < 0.035 and x_pom < 0.01. The relative contribution of diffractive events
to the inclusive D*+/-(2010) photoproduction cross section is about 6%. The
data are in agreement with perturbative QCD calculations based on various
parameterisations of diffractive parton distribution functions. The results are
consistent with diffractive QCD factorisation.
