  We use the color-octet mechanism combined with the two gluon exchange model
for the diffractive $J/\psi$ production in resolved photon processes. In the
leading logarithmic approximation in QCD, we find that the diffractive $J/\psi$
production cross section is related to the off-diagonal gluon density of the
proton, the gluon density of the photon and to the nonperturbative color-octet
$^3 S_{1}^{(8)}$ matrix element of $J/\psi$. The cross section is found to be
very sensitive to the gluon density of the photon. As a result, this process
may provide a wide window for testing the two-gluon exchange model, studying
the nature of hard diffractive factorization breaking and may be particularly
useful in studying the gluon distribution of the photon. And it may also be a
golden place to test the color-octet mechanism proposed by solving the
$\psi'(J/\psi)$ surplus problem at the Tevatron.
