  We consider the phonon contribution to the bulk viscosities $\zeta_1,
\zeta_2$ and $\zeta_3$ of a cold relativistic superfluid. We assume the low
temperature $T$ regime and that the transport properties of the system are
dominated by the phonons. We use kinetic theory in the relaxation time
approximation and the low energy effective field theory of the corresponding
system. The parametric dependence of the bulk viscosity coefficients is fixed
once the equation of state is specified, and the phonon dispersion law to cubic
order in momentum is known. We first present a general discussion, valid for
any superfluid, then we focus on the color-flavor locked superfluid because all
the parameters needed in the analysis can be computed in the high density limit
of QCD, and also because of the possible astrophysical applications. For the
three independent bulk viscosity coefficients we find that they scale with the
temperature as $\zeta_i \sim 1/T$, and that in the conformal limit only the
third coefficient $\zeta_3$ is non-zero.
