The hydrothermal reactions of a bent ligand, 1H-3,5-bis(4-pyridyl)-1,2,4-triazole (bpt), with Co/Ni(II) ions as well as a series of polycarboxylate co-ligands yielded five new coordination polymers, namely, {[Co2(fum)2(bpt)2(H2O)]·3H2O}n (1), {[Co(mal)(bpt)0.5(H2O)]·1.5H2O}n (2), {[Co2(bptc)(bpt)2(EtOH)(H2O)2]·2H2O}n (3), [Ni2(btc)(bpt)2(H2O)2]·6H2O (4), [Ni2(Hbidc)2(bpt)2]·7H2O (5) (here, H2fum = fumaric acid, H2mal = malonic acid, H4bptc = 3,3′,4,4′-benzophenone-tetracarboxylate acid, H4btc = 1,2,4,5-benzenetetracarboxylate acid, H3bidc = 1H-benzimidazole-5,6-dicarboxylic acid). These complexes exhibit different architectures and magnetic behaviors: 1 has a 3D (3,5)-connected (42·6)(42·65·83) topology, showing field-induced spin-flop transition; 2 and 3 both have a (3,4)-connected topology, exhibiting normal antiferromagnetism, with a 3D (63)(63·83) symbol for 2and a 2D (62·8)2(64·82) symbol for 3, respectively. In 4 and 5, the topological analysis results reveal that 4 can be simplified to a 3D 4-connected NbO net, while 5 is a 3D trinodal (3,4,6)-connected (63)(65·8)(612·8·102) net. Both 4 and 5 exhibit spin-canted antiferromagnetism.