We present a study of diffractive associated J/ψ + γ production at the Fermilab Tevatron and LHC based on the Ingelman-Schlein model for hard diffractive scattering and the factorization formalism of NRQCD for quarkonia production. we find that this process (p +p → p + J/ψ + γ + X) can be used to probe the gluon content of the Pomeron and test the assumption of diffractive hard scattering factorization. Using the renormalized Pomeron flux factor D ≃ 0.11(0.052) , the single diffractive J/ψ + γ production cross section at 4 < P T < 10 GeV , −1 < η < 1 region is found to be of the order of 3.0pb (8.5 pb ). The ratio of single diffractive to inclusive production is 0.50%(0.15%) in central region at the Tevatron (LHC) for the gluon fraction in the Pomeron f g = 0.7, independent of the values of color-octet matrix elements. PACS number(s): 12.40Nn, 13.85.Ni, 14.40.Gx