In this paper we analyze the photoproduction of heavy quarkonia pairs which include b-quarks, such as B_{c}^{+}B_{c}^{-}-mesons or charmonium-bottomonium pairs. Compared to charmonia pair production, these channels get contributions only from some subsets of diagrams, and thus allow for a better theoretical understanding of different production mechanisms. In contrast to the production of hidden-flavor quarkonia, for the production of B_{c}-meson pairs there are no restrictions on internal quantum numbers in the suggested mechanisms. Using the Color Glass Condensate approach, we estimated numerically the production cross-sections in the kinematics of the future electron–hadron colliders and the ultraperipheral collisions at LHC. We found that the production of J/psi ,eta _{c} and B_{c}^{+}B_{c}^{-} meson pairs are the most promising channels for studies of quarkonia pair production.