  We study low-temperature transport through carbon nanotube quantum dots in
the Coulomb blockade regime coupled to niobium-based superconducting leads. We
observe pronounced conductance peaks at finite source-drain bias, which we
ascribe to elastic and inelastic cotunneling processes enhanced by the
coherence peaks in the density of states of the superconducting leads. The
inelastic cotunneling lines display a marked dependence on the applied gate
voltage which we relate to different tunneling-renormalizations of the two
subbands in the nanotube. Finally, we discuss the origin of an especially
pronounced sub-gap structure observed in every fourth Coulomb diamond.
