The reactions of cobalt(II) nitrate with 4,7-di(1,2,4-triazol-1-yl)-2,1,3-benzothiadiazole (Tr(2)btd) and aromatic dicarboxylic acids (terephthalic (H(2)bdc), 2,6-naphthalenedicarboxylic (2,6-H(2)ndc), and 2,5-furandicarboxylic (2,5-H(2)fdc) acids) afford metal-organic frameworks [Co(Tr(2)btd)(bdc)]n (I) and {[Co-2(Tr(2)btd)(DMF)(2,6-ndc)(2)]center dot DMF}n (II) with the layered structures and chain metal-organic framework [Co(Tr(2)btd)(2)(H2O)(2,5-fdc)](n) (III). Compounds I and III are paramagnetic in a temperature range of 1.77-300 K without exchange interactions between the Co-2+ cations, and compound II exhibits the antiferromagnetic interaction between the Co2+ cations in the binuclear building blocks with the exchange interaction constant J approximate to -100 K. Single crystals of the phase of compound IIIa with the identical composition but different structure are found when taking samples for X-ray diffraction (XRD) analysis. The molecular structures of metal-organic frameworks I, II, III, and IIIa are determined by XRD (CIF files CCDC nos. 2343141 (I), 2343297 (II), 2343296 (III), and 2343140 (IIIa)).