Two new Co(II) and Ni(II) coordination polymers viz. [Co(H2O)2(μ-fum)(3-CNpy)2]n (1) and {[Ni(H2O)2(μ-succ)(4-CNpy)2]·2H2O}n (2) (where, fum= fumarate, CNpy = cyanopyridine, succ = succinate) have been synthesized and characterized using single crystal XRD, elemental analysis, spectroscopic (IR and electronic) techniques and TGA. Compound 1 crystallizes as a fumarato bridged Co(II) polymer; whereas, compound 2 is a succinato bridged Ni(II) polymer. The presence of various non-covalent interactions in the compounds stabilizes the layered assemblies of the compounds. Antiparallel nitrile∙∙∙nitrile interactions are observed in both the crystal structures involving the nitrile moieties of coordinated CNpy which provide rigidity to the compounds. Further analysis reveals that the N-atom of –CN group of 3-CNpy in 1 is involved in unusual N(nitrile)∙∙∙π(fum) interactions with the π-electrons of the C=C bond of fum. Enclathrated (H2O)2 cores within the supramolecular host cavity of compound 2 provides additional reinforcement to the crystal structure. We have also carried out theoretical studies to analyze the π-stacking and H-bonding interactions present in the crystal structure of compound 1 using quantum theory of atoms-in-molecules (QTAIM), non-covalent interaction plot (NCI plot) and molecular electrostatic potential (MEP) surface analysis. The MEP value at the N-atom of the cyano group of 1 is negative and the value is neutral over the double bond of the fum; indicating the possibilities of formation of N(nitrile)∙∙∙π(fum) interactions. Energetic analysis suggests that antiparallel π-stacking observed between the 3-CNpy moieties in 1 is the most dominating force followed by N(nitrile)∙∙∙π(fum) interaction and finally the H-bonds.