  If tan(beta) is large, down-type quark mass matrices and Yukawa couplings
cannot be simultaneously diagonalized, and flavour violating couplings of the
neutral Higgs bosons are induced at the 1-loop level. These couplings lead to
Higgs-mediated contributions to the decays B_s -> mu+ mu- and B_d -> tau+ tau-,
at a level that might be of interest for the current Tevatron run, or possibly,
at B-factories. We evaluate the branching ratios for these decays within the
framework of minimal gravity-, gauge- and anomaly-mediated SUSY breaking
models, and also in SU(5) supergravity models with non-universal gaugino mass
parameters at the GUT scale. We find that the contribution from gluino loops,
which seems to have been left out in recent phenomenological analyses, is
significant. We explore how the branching fraction varies in these models,
emphasizing parameter regions consistent with other observations.
