  In this paper we study the high energy exclusive photoproduction of heavy
quarkonia pairs in the leading order of the strong coupling constant
$\alpha_{s}$. In the suggested mechanism the quarkonia pairs are produced with
opposite charge parities, and have predominantly oppositely directed transverse
momenta. Using the Color Glass Condensate approach, we estimated numerically
the production cross-sections in the kinematics of the forthcoming
electron-proton colliders, as well as proton-ion colliders in ultraperipheral
collisions. We found that the cross-sections are within the reach of planned
experiments and can be measured with reasonable precision. The suggested
mechanism has significantly larger cross-section than that of the same
$C$-parity quarkonia pair production.
