  We show that introducing subnucleon scale fluctuations constrained by HERA
diffractive $J/\Psi$ production data significantly affects the incoherent
diffractive $J/\Psi$ production cross section in ultraperipheral heavy ion
collisions. We find that the inclusion of the additional fluctuations increases
the ratio of the incoherent to the coherent cross section approximately by a
factor of $2$, and modifies the transverse momentum spectra of the produced
$J/\Psi$ at momenta larger than the scale that corresponds to the distance
scale of the subnucleonic fluctuations. We present predictions for $J/\Psi$
production in ultraperipheral heavy ion collisions at $\sqrt{s_{NN}}=5.02\,{\rm
TeV}$ at the LHC and $200\,{\rm GeV}$ at RHIC.
