We study theoretically the properties of the ground state of a mescopic ring with a seriescoupled double quantum dot in the Kondo regime by means of the two-inpurity Anderson Hamiltonian. The Hamiltonian is solved by means of the slave-boson mean-field theory. It is shown that two dots can be coupled coherently, which is reflected in the appearance of parity effects and the complex current-phase relation in this system. This system might be a possile candidate for future device applications.