  We extend our approach based on the second order perturbation theory in the
Coulomb interaction recently developed for quantum dots coupled to
superconducting leads to the superconducting double quantum dot setups. Using
our perturbative method we evaluate several single-particle quantities such as
on-dot induced gap and generalized occupations together with the Andreev in-gap
spectra and compare them with numerically exact results from the Numerical
Renormalization Group and Quantum Monte Carlo finding a very good
correspondence for not too strongly correlated regimes. Thus we can offer in a
wide parameter range this method as an efficient and reliable alternative to
the heavy numerical tools exclusively used so far for the description of such
experimentally relevant systems.
