Coordination polymers with external stimuli-responsive structural transformation acquired paramount importance in the advanced material research field due to their eye-catching application to deal with the existing challenging issue, and Co(II) metal complex with d7 electronic configuration is a renowned candidate for kinetic accountability and has the potentiality of structural transformation. Bearing these factors in mind, here, a Co(II) congener of a previously reported high hydrogen-adsorbing Cu(II)-based coordination polymer (CP), {[Cu(4-bpe)(2-ntp)]}n [where 2-ntp2- = 2-nitroterephthalate and 4-bpe = 1,2-bis-(4-pyridyl)ethane], has been synthesized to study the metal change impact on hydrogen adsorption and solvent-induced structural transformation with their impact on hydrogen uptake. This modified framework has a 2D + 2D → 3D inclined polycatenated framework as comparable to our previously published Cu(II) framework. Here, on the variation of different solvents, the labile Co(II)-containing framework exhibits a structural change through single-crystal to single-crystal (SC-SC) structural transformation and results in three new framework structures. All four frameworks are structurally characterized by elemental analysis, IR, PXRD, TGA, and single-crystal X-ray diffraction. The desolvated parent framework with exposed metal centers exhibits excellent results of H2 adsorption of 1.3 wt % (145 cc/g) at 77 K and pressure of 1 bar with structural sustainability and CO2 uptake of 130 cc/g at 195 K and 1 bar. For the other three solvent-mediated structural derivatives, H2 and CO2 adsorption have been studied, and the results are correlated with their structure.