  The flavour-changing neutral current transition b \to s can serve as a
sensitive probe of WIMP dark matter models, if the WIMP mass is under 2 GeV. In
this work we extend our earlier analysis to a generic class of models where the
interaction between the dark matter sector and the Standard Model matter sector
is mediated by the Higgs boson(s). We show that experimental limits on the
decays of B-mesons to K(K^*) and missing energy provide stringent constraints
on the parameter space of such models, but do not rule out sub-GeV WIMPs in a
model-independent way. We find that in the context of the NMSSM with light
pseudoscalar Higgs, the WIMP masses under a few hundred MeV are generically
excluded with the exception of few highly tuned points in the parameter space.
