  We study an interacting quantum dot in contact with a superconducting island
described by the Richardson model with a Coulomb repulsion term controlling the
number of electrons on the island. This Hamiltonian admits a compact
matrix-product-operator representation and can be efficiently and accurately
solved using the density-matrix renormalization group. We systematically
explore the effects of the charging energy $E_c$. For $E_c$ comparable to the
superconducting gap $\Delta$, the subgap states are stabilized by the
combination of Kondo exchange coupling and charge redistribution driven by the
Coulomb interaction. The subgap states exist for both even and odd
superconductor ground-state occupancy, but with very distinctive excitation
spectra in each case. The spectral peaks are not symmetric with respect to the
chemical potential and may undergo discontinuous changes as a function of gate
voltages.
