  Bilayer graphene has two non-equivalent sublattices and, therefore, the same
adatom impurity can manifest in spectrally distinct ways-sharp versus broad
resonances near the charge neutrality-depending on the sublattice it adsorbs
at. Employing Green's function analytical methods and the numerical Kwant
package we investigate the spectral and transport interplay between the
resonances and superconducting coherence induced in bilayer graphene by
proximity to an s-wave superconductor. Analyzing doping and temperature
dependencies of quasi-particle spin-relaxation rates, energies of
Yu-Shiba-Rusinov states, Andreev spectra and the supercurrent characteristics
of Josephson junctions we find unique superconducting signatures discriminating
between resonant and off-resonant regimes. Our findings are in certain aspects
going beyond the superconducting bilayer graphene and hold for generic s-wave
superconductors functionalized by the resonant magnetic impurities.
