  We use the present upper bound on the neutron electric dipole moment to give
an estimate for the upper limit of the CP-violating couplings of the
$\eta(\eta')$ meson to the neutron. Using this result, we derive constraints on
the CP-violating two-pion decays of the $\eta(\eta')$. Our results are relevant
for the running and planned GlueX and LHCb measurements of rare meson decays.
