To explore the influence of different N-donor auxiliary ligands on the self-assembly and structures of Co^II-based coordination polymers (CPs), six coordination compounds, formulated as {Co(dnpdc)(bipy)}_n (1), {[Co₃(dnpdc)₃(bipy)₃(H₂O)₂]·2H₂O}_n (1s), {[Co₅(OH)₂(dnpdc)₄(bpp)₂(H₂O)₂]·2H₂O}_n (2), {[Co₅(OH)₂(dnpdc)₄(bpp)₂(H₂O)₂]·2H₂O}_n (3), {Co(dnpdc)(bcim)·(H₂O)_0.5}_n (4) and {Co₂(dnpdc)₂(bpee)(bpim)}_n (5) where bipy = 4,4′-bipyridine, bpee = bis(4-pyridyl)ethene, bpp = 1,3-bis(4-pyridyl)propane, bimb = 1,4-bis(imidazolyl)benzene, bcim = 4-bis(imidazol-1-ylmethyl)benzene and bpim = 4,4′-bis(imidazolyl)biphenyl, have been rationally designed and generated through the hydrothermal reaction of the dicarboxylate derivative ligand (H₂dnpdc), Co(NO₃)₂, and a series of different N-donor co-ligands. These N-donor ligands were employed in the crystal preparation of these CPs as structure-directing ligands owing to their structural specialties and size-matching fashions. X-ray analyses revealed that these compounds exhibit two- or three-dimensional architectures. Compounds 1 and 5 are iso-structural, and both exhibit 3D “pillared” frameworks based on 1D [Co(OCO)₂]_n chains. Compound 1s, prepared at higher temperature, displays unusual (4,6)-connected and three-fold interpenetrated frameworks based on mononuclear and dinuclear nodes. Compound 2 features a new 10-connected 3D topology net based on a novel Co₅(μ-OH)₂(μ-OCO)₆ pentanuclear cluster linked by mixed bpp and dnpdc ligands. Compound 3 exhibits a 6-fold interpenetrated diamond net. Compound 4 shows 2D sheets constructed from flexible bcim and dnpdc ligands. The magnetic properties of compounds 1, 2 and 5 have also been investigated to help us tentatively understand their structure–property relationships.