Precise modulation of the structure and magnetic properties of coordination compounds is of great importance in the development of framework magnetic materials. Herein, we report that the coordination self-assembly of a neutral cobalt(ii) magnetic building block and selective pyridine derivatives as organic linkers has led to two distinct cobalt(ii) coordination polymers, {Co(DClQ)2(bpy)}n (1) and {Co2(DClQ)4(tpb)}n (2) (DClQ = (5,7-dichloro-8-hydroxyquinoline; bpy = 4, 4′-dipyridine; tpb = 1,2,4,5-tetra(4-pyridyl)benzene)). Structural analyses revealed that 1 and 2 are one-dimensional (1D) and 2D coordination polymers containing the same neutral magnetic building block [Co(DClQ)2] bridged by bitopic bpy and tetratopic tpb ligands, respectively. Both the complexes have a distorted octahedral CoN4O2 coordination geometry around each cobalt center offered by the bidentate ligand and organic linkers. Magnetic studies reveal large easy-plane and easy-axis magnetic anisotropy for 1 and 2, respectively. However, because of the weak antiferromagnetic coupling between the bpy-bridged CoII centers, no slow relaxation of the magnetization was observed in 1 under both zero or applied dc fields. Interestingly, complex 2 exhibits slow magnetic relaxation under external fields, indicative of a framework single-ion magnet of 2. Theoretical calculations further support the experimental results and unveil that the D values are +65.3 and -91.2 cm-1 for 1 and 2, respectively, while the magnetic exchange interaction was precisely estimated as -0.16 (1) and -0.009 (2) cm-1. The foregoing results show that the structural dimensionality and magnetic properties can be rationally modified via pre-designed magnetic building blocks and a suitable choice of organic bridging ligands. This journal is © The Royal Society of Chemistry.