In this work, six Co^II coordination polymers (CPs) based on a new semi-rigid methylene-bridged bis-pyridyl-bis-amide ligand N,N′-bis(4-methylenepyridin-4-yl)-2,6-naphthalenedicarboxamide (4-bmpnd) and various polycarboxylates, namely [Co(4-bmpnd)(5-HMIP)₂(H₂O)₂] (1), [Co₂(4-bmpnd)₂(5-NIP)₂(H₂O)]·2H₂O (2), [Co₂(4-bmpnd)(5-AIP)₂(H₂O)]·2H₂O (3), [Co(4-bmpnd)_0.5(1,4-CHDC)]·H₂O (4), [Co(4-bmpnd)(1,4-NDC)(H₂O)₂]·2DMF (5), and [Co(4-bmpnd)(1,2,4,5-BTA)_0.5(H₂O)] (6) (5-H₂MIP = 5-methylisophthalic acid, 5-H₂NIP = 5-nitroisophthalic acid, 5-H₂AIP = 5-aminoisophthalic acid, 1,4-H₂CHDC = 1,4-cyclohexanedicarboxylic acid, 1,4-H₂NDC = 1,4-naphthalenedicarboxylic acid, and H₄BTA = 1,2,4,5-benzenetetracarboxylic acid) have been constructed by a hydrothermal/solvothermal method. Their structures are characterized by infrared spectroscopy, powder X-ray diffraction and single-crystal X-ray diffraction. CP 1 has a 1D linear structure. CP 2 displays a 2D 4-connected wave network. CP 3 exhibits a 2D sandwich-type structure. CP 4 can be described as a 4-connected 2D grid-like structure. CP 5 shows a 4-connected 3D cds framework with the topological symbol of {6⁵·8}. CP 6 is a (4,4)-connected 3D framework with the {4·6⁴·8}₂{4²·10⁴} topology. The effects of functional groups and the number of the carboxyl groups of polycarboxylates on the structures of the title coordination polymers were discussed. The photocatalytic properties of CPs 1–6 were studied under UV irradiation, which have good photocatalytic degradation performance for anionic dye Congo red (CR). The possible photocatalytic mechanism was explored.