  We study the exclusive diffractive $c \bar c$ photoproduction in
ultraperipheral $pA$ collisions. The formalism makes use of off-diagonal
generalizations of the unintegrated gluon distribution, the so-called
generalized transverse momentum dependent distributions (GTMDs). We present two
different formulations. The first one is based directly on gluon GTMD
parametrizations in momentum space. Another option is the calculation of the
GTMD as a Fourier transform of the dipole-nucleon scattering amplitude
$N(Y,\vec{r}_{\perp},\vec{b}_{\perp})$. The latter approach requires some extra
regularization discussed in the paper. Different dipole amplitudes from the
literature are used. Compared to previous calculations in the literature, we
integrate over the full phase space and therefore cross sections for realistic
conditions are obtained. We present distributions in rapidity of $c$ or $\bar
c$, transverse momentum of the $c \bar c$ pair, four-momentum transfer squared
as well as the azimuthal correlation between a sum and a difference of the $c$
and $\bar c$ transverse momenta. The azimuthal correlations are partially due
to the so-called elliptic gluon Wigner distribution. Different models lead to
different modulations in the azimuthal angle. The modulations are generally
smaller than 5%. They depend on the range of transverse momentum selected for
the calculation.
