  We calculate the cross section for $c\bar{c}g$-production in diffractive DIS
with finite quark masses at zero momentum transfer $t$. The calculation is done
in the leading log(1/$x_{P}$) approximation and is valid in the region of high
diffractive masses $M$ (small $\beta$). We apply our cross section formula
including both $c{\bar c}$- and $c\bar{c}g$ in a Monte Carlo simulation to
diffractive $D^{*\pm}$ meson production at HERA. We compare our predictions to
results of H1 using three parameterizations for the unintegrated gluon density.
