We report the formation of one- and two-dimensional metal-organic coordination structures from para-hexaphenyl-dicarbonitrile (NC-Ph6-CN) molecules and Cu atoms on graphene epitaxially grown on Ir(111). By varying the stoichiometry between the NC-Ph6-CN molecules and Cu atoms, the dimensionality of the metal-organic coordination structures could be tuned: for a 3:2 ratio, a two-dimensional hexagonal porous network based on threefold Cu coordination was observed, while for a 1:1 ratio, one-dimensional chains based on twofold Cu coordination were formed. The formation of metal-ligand bonds was supported by imaging the Cu atoms within the metal-organic coordination structures with scanning tunneling microscopy. Scanning tunneling spectroscopy measurements demonstrated that the electronic properties of NC-Ph6-CN molecules and Cu atoms were different between the two-dimensional porous network and one-dimensional molecular chains.