  We present a study of leptonic $B$ meson decay constants in lattice QCD with
two flavors ($N_f=2$) of light dynamical quarks using NRQCD for the heavy
quark. Gauge configurations are generated with a renormalization-group improved
gauge action and a meanfield-improved clover light quark action. Measurements
are carried out at two values of $\beta=6/g^2$, each for four sea quark masses,
corresponding to the inverse lattice spacing $a^{-1}\approx 1.3$ and 1.8 GeV in
the chiral limit of sea quark. The continuum values of the decay constants are
derived by evaluating the discretization errors at each finite lattice spacing.
We find $f_B^{N_f=2}=204(8)(29)(+44) $ MeV, $f_{B_s}^{N_f=2} = 242(9)(34)(+38)$
MeV, and $f_{B_s}^{N_f=2}/f_B^{N_f=2} = 1.179(18)(23)$, where the errors listed
are statistical, systematic and uncertainty due to choice of the physical
quantity used to fix the scale. Comparison is made to quenched results
($N_f=0$) obtained with the same action combination and matching lattice
spacings. We find $f_B^{N_f=2}/f_B^{N_f=0}=1.07(5)$,
$f_{B_s}^{N_f=2}/f_{B_s}^{N_f=0}=1.10(5)$ and
$(f_{B_s}/f_B)^{N_f=2}/(f_{B_s}/f_B)^{N_f=0}=1.03(2)$, which indicates a 5--10%
increase in the values of the decay constants, but no appreciable change in the
ratio $f_{B_s}/f_B$, due to sea quarks.
