  The study of exclusive processes in the future electron-ion ($eA$) colliders
will be an important tool to investigate the QCD dynamics at high energies as
they are in general driven by the gluon content of the target which is strongly
subject to parton saturation effects. In this paper we compute the coherent and
incoherent cross sections for the deeply virtual Compton scattering (DVCS)
process relying on the color dipole approach and considering different models
for the dipole - proton scattering amplitude. The dependencies of the cross
sections with the energy, photon virtuality, nuclear mass number and squared
momentum transfer are analysed in detail. We demonstrate that the ratio between
the incoherent and coherent cross sections decreases at smaller values of $Q^2$
and increases at smaller values of $A$. We show that the coherent cross section
dominates at small $t$ and exhibits the typical diffractive pattern, with the
number of dips in the range $|t| \le 0.3$ GeV$^2$ increasing with the mass
atomic number. Our results indicate that the position of the dips are
independent of the model used to treat the dipole - proton interaction as well
as of the center-of-mass energy.
