  In this paper we analyze the exclusive photoproduction of heavy quarkonia
pairs in the collinear factorization framework. We evaluate the amplitude of
the process for $J/\psi\,-\eta_{c}$ quarkonia pair in the leading order of the
strong coupling $\alpha_{s},$ and express it in terms of generalized parton
distributions (GPDs) of gluons in the proton. We made numerical estimates in
the kinematics of the Electron Ion Collider, and found that in the
photoproduction regime, when the virtuality of the photon is much smaller than
the quarkonia mass, the cross-section of the process is sufficiently large for
experimental studies. We demonstrate that the study of this channel can
complement existing studies of gluon GPDs from other channels.
