  BiOCuS is a band insulator that becomes metallic upon hole doping.
Superconductivity was recently reported in doped BiOCu$_{1-x}$S and attributed
to spin fluctuations as a pairing mechanism. Based on first principles
calculations of the electron-phonon coupling, we argue that the latter is very
strong in this material, and probably drives superconductivity, which is
however strongly depressed by the proximity to magnetism. We find however that
BiOCu$_{1-x}$S is a quite unique compound where both a conventional
phonon-driven and an unconventional triplet superconductivity are possible, and
compete with each other. We argue that, in this material, it should be possible
to switch from conventional to unconventional superconductivity by varying such
parameters as doping or pressure.
