This article further develops the Coulson-Fischer formalism in conjunction with the optimised effective potential method V.N. Glushkov and S. Wilson, Molec. Phys. 110, 149 (2012) to incorporate both exchange and static correlation effects for excited states having the same symmetry as the ground state. By using this formalism, we compute complete potential energy curves for the ground and first excited states of the molecule and the isoelectronic heteronuclear ion. Effective potentials are generated in according to a novel density functional theory A.K. Theophilou, J. Chem. Phys. 149, 074104 (2018) in which the Kohn-Sham (KS) like potential has spherical symmetry around each nucleus. In this way, the inconsistencies of standard density functional theory concerning the asymmetry of the KS potential are remedied. In our implementation, an effective potential which satisfies this requirement is expressed as a direct mapping of the external potential. Different approximations for the effective potentials are investigated. It is shown that applications of the proposed formalism support good agreement with the exact Coulson-Fischer theory for both the ground and first excited state potential energy curves and thus a qualitatively correct description of dissociation.