  The $r$-modes of accreting neutron stars could be a detectable source of
persistent gravitational waves if the bulk viscosity of the stellar matter can
prevent a thermal runaway. This is possible if exotic particles such as
hyperons are present in the core of the star. We compute bulk viscous damping
rates and critical frequencies for $r$-modes of neutron stars containing
hyperons in the framework of relativistic mean field theory. We combine the
results of several previous calculations of the microphysics, include for the
first time the effect of rotation, and explore the effects of various
parameters on the viability of persistent gravitational wave emission. We find
that persistent emission is quite robust, although it is disfavored in stars
below 1.3--1.5 $M_\odot$ depending on the equation of state. In some cases
persistent emission is compatible with temperatures as low as $10^7$ K,
observed in some accreting neutron stars in quiescence.
