  We present results for the B_s meson decay constant f_{B_s} from simulations
at three lattice spacings in the range a^{-1}=1.1 to 2.6 GeV using NRQCD heavy
quarks and clover light quarks in the quenched approximation. We study scaling
of this quantity and check the consistency between mesons decaying from rest
and from a state with nonzero spatial momentum. The cancellation of power law
contributions that arise in the NRQCD formulation of heavy-light currents is
discussed. On the coarsest lattice the D_s meson decay constant f_{D_s} is
calculated. Our best values for the decay constants are given by f_{B_s} =
187(4)(4)(11)(2)(7)(6) MeV and f_{D_s} = 223(6)(31)(38)(23)(9)(^{+3}_{-1}) MeV.
