  With an increasing number of experiments observing phonon thermal Hall effect
in magnets, it is theoretically desired to have a minimal model for the phonon
thermal Hall effect. In this work, we study a simple model of acoustic phonons
and uncorrelated paramagnetic doublets. When the doublets are non-Kramers, a
linear pseudospin-phonon coupling is allowed by time-reversal symmetry and
yields resonant phonon-pseudospin scattering. We compute the thermal
longitudinal and Hall conductivities of the model and found qualitative
agreement with recent experiments in $\rm{Pr}_2\rm{Ir}_2\rm{O}_7$ [Uehara et
al.,Nat Commun 13, 4604 (2022)].
