  We study the sensitivity of the stopped pion source of neutrinos at the
Spallation Neutron Source (SNS) at Oak Ridge National Laboratory to neutrino
non-standard interactions (NSI). In particular, we find that simple event
counting above threshold can improve constraints on NSI for electron- and muon-
flavored NSI, with the strongest constraints arising for flavor-diagonal NSI
coupling to $\mu$ neutrinos. However, if the detector resolution is sufficient
to all for even a coarse spectral study of events, COHERENT will also be
sensitive to the mass scale of NSI. We demonstrate that this can yield new
limits on $Z'$ completions of NSI if the gauge boson mass is $\lesssim 1$ GeV.
