  We study the direct detection rate for SUSY cold dark m atter (CDM) predicted
by the minimal supersymmetric standard model with universal boundary conditions
and large values for tan\beta. The relic abundance of the lightest
supersymmetric particle (LSP), assumed to be approximately a bino, is obtained
by including its coannihilations with the next-to-lightest supersymmetric
particle (NLSP), which is the lightest s-tau. We find detectable rates in the
currently planned experiments for a sector of the parameter space consistent
with the cosmological constraint on the LSP relic abundance and the ones
imposed by b->s gamma and the Higgs searches.
