Two Co2+ metal-organic framework materials, constructed from a combination of 1,4-benzenedicarboxylate (BDC) and either 2,2′-dipyridyl-N-oxide (DPNO) or 2,2′-dipyridyl-N,N′-dioxide (DPNDO), are synthesized under solvothermal reaction conditions, and their structures solved by single crystal X-ray diffraction. Both have three-dimensional structures that contain octahedral Co2+ centers with μ2-(η2)-BDC, and bidentate DPNO or DPNDO coligands that bridge pairs of metal centers but do not contribute toward the overall connectivity of the framework. Co3(BDC)3(DPNO)2 contains trimers of trans corner-shared Co-centered octahedra with one type of bridging BDC ligand forming terminal edges of the trimers, bridging to neighboring trimer units, and a second type, bridging pairs of metals and also connecting neighboring trimers. Co2(BDC)2(DPNDO) is constructed from one-dimensional inorganic chains consisting of cis- and trans-corner shared Co2+-centered octahedra. The DPNDO ligand is bis-bidentate, forming the edges of one type of octahedron and the trans corners of the second type, with the coordination for both octahedra completed by bridging BDC linkers, which in turn connect the inorganic chains to yield a three-dimensional structure. Thermogravimetric analysis shows both materials contain trapped solvent, and while Co3(BDC)3(DPNO)2 is unstable with respect to solvent loss, Co2(BDC)2(DPNDO), and its magnesium analogue, can be desolvated to yield permanently porous materials that show thermal stability up to 300 °C. For Co2(BDC)2(DPNDO), gas adsorption studies show permanent microporosity with moderate uptake of small gas molecules (N2, CO2, CH4, and C2H6), supported by Grand Canonical Monte Carlo calculations based on the assumption of rigid crystal structures, while gravimetric analysis shows rapid and reversible methanol adsorption at ambient pressure for both the Co and Mg analogues of the framework.