Three coordination compounds with dimensions from 0D to 2D, namely, [Co(bppdca)2(HL1)2] (1) [Co(bppdca)(L2)(H2O)]·2H2O (2) and [Co(bppdca)(L3)]·3H2O (3) [bppdca = N,N′-bis(pyridine-3-yl)pyridine-2,6-dicarboxamide, H2L1 = 2,5-pyridinedicarboxylic acid, H2L2 = 4,4′-oxybisbenzoic acid, H2L3 = 2-carboxymethylsulfanyl nicotinic acid] were hydrothermally synthesized and structurally characterized. Single crystal X-ray diffraction analysis reveals that complex 1 is a discrete 0D complex, in which the bppdca ligand and the H2L1 act as the terminal groups to coordinate with the CoII ions. In coordination polymer 2, two bppdca ligands coordinate in anti configuration with two CoII ions to generate a 28-membered Co2(bppdca)2 loop, which is further extended into 1D ladder-like double chain by pairs of L2 ligands. In 3, the CoII ions are linked by bppdca ligands to generate 1D wave-like chain, which is further connected by the L3 to form a 2D network. Finally, the coordination compounds 1–3 are extended into 3D supramolecular frameworks through the hydrogen bonding interactions. The CoII ions and the bppdca ligands in the title coordination compounds exhibit different coordination characters and conformations. The effect of organic dicarboxylates with different rigidity and length on the structures of CoII coordination compounds was investigated. In addition, the fluorescence and electrochemical behaviors of coordination compounds 1–3 were reported.