  We present a correlated analysis for the $\Delta B =1, 2$ processes which
occur via $b\to s$ transitions within models with a family non-universal
$U(1)^\prime$. We take a model-independent approach, and only require family
universal charges for the first and second generations and small fermion mixing
angles. The results of our analysis show that within this class of models, the
anomalies in $B_s - \bar B_s$ mixing and the time-dependent CP asymmetries of
the penguin-dominated $B_d \to (\pi, \phi, \eta', \rho, \omega, f_0)K_S$ decays
can be accommodated.
