  The COHERENT collaboration searched for scalar dark matter particles produced
at the Spallation Neutron Source with masses between 1 and 220~MeV/c$^2$ using
a CsI[Na] scintillation detector sensitive to nuclear recoils above
9~keV$_\text{nr}$. No evidence for dark matter is found and we thus place
limits on allowed parameter space. With this low-threshold detector, we are
sensitive to coherent elastic scattering between dark matter and nuclei. The
cross section for this process is orders of magnitude higher than for other
processes historically used for accelerator-based direct-detection searches so
that our small, 14.6~kg detector significantly improves on past constraints. At
peak sensitivity, we reject the flux consistent with the cosmologically
observed dark-matter concentration for all coupling constants $\alpha_D<0.64$,
assuming a scalar dark-matter particle. We also calculate the sensitivity of
future COHERENT detectors to dark-matter signals which will ambitiously test
multiple dark-matter spin scenarios.
