  We study the Josephson coupling between two superconductors through a single
correlated molecular level, including Coulomb interaction on the level and
coupling to a bosonic environment. All calculations are done to the lowest,
i.e., the fourth, order in the tunneling coupling and we find a suppression of
the supercurrent due to the combined effect of the Coulomb interaction and the
coupling to environmental degrees of freedom. Both analytic and numerical
results are presented.
