Based on a terpyridine derivative and two different dicarboxylate ligands, two new cobalt(ii) coordination polymers, namely [Co(pytpy)(DClbdc)]n (1) and [Co(pytpy)(ndc)]n (2) (pytpy = 4′-(4-pyridyl)-2,2′:6′,2′′-terpyridine, H2DClbc = 2,5-dichloroterephthalic acid, and H2ndc = 2,6-naphthalenedicarboxylic acid), were hydrothermally synthesized and characterized structurally and magnetically. Single-crystal X-ray diffraction revealed that 1 and 2 are one-dimensional (1D) linear and zigzag chain complexes, respectively, with the Co2+ centers located in a compressed and an elongated bipyramid of 1 and 2, respectively. Magnetic investigation revealed that the chain complexes exhibit distinct easy-axis and easy-plane magnetic anisotropy with D = −95.6 and −42.8 cm−1 for 1 and 2, respectively. The inverse magnetic anisotropy of 1 and 2 was further confirmed and understood using ab initio calculations. Interestingly, field-induced single-ion magnet (SIM) behaviors were evidenced at low temperatures with the effective energy barrier of Ueff = 27.3 and 12.7 cm−1 for 1 and 2, respectively. The foregoing results provide not only a way for the construction of 1D cobalt(ii) coordination polymers with slow magnetic relaxation behavior but also a chance to tune chain topologies and magnetic anisotropy in one-dimensional coordination polymers via different dicarboxylates. © 2022 The Royal Society of Chemistry