  The known ratio of the branching fractions for D_s^* --> D_s pi^0 and D_s^*
--> D_s gamma may be used to extract the coupling of eta mesons to strange
quarks once the value of the pi^0-eta mixing angle is known. This requires that
realistic models for the spectra as well as the magnetic dipole (M1) decays of
the heavy-light (Q qbar) mesons are available. The coupling of eta mesons to
light quarks may then be estimated using SU(3) flavor symmetry. Applied to the
quark model for the baryons, an eta NN pseudovector coupling constant of f_{eta
NN} = 0.35^{+0.15}_{-0.25} is obtained. If the charm quark couples
significantly to the eta meson, as is suggested by the decay mode psi' -->
J/(psi eta), then somewhat larger values of f_{eta NN} can be obtained. These
values are sufficiently small to be consistent with phenomenological analysis
of photoproduction of the eta on the nucleon and the reaction pp --> pp eta.
