  Effective neutrino-quark generalized interactions are entirely determined by
Lorentz invariance, so they include all possible four-fermion non derivative
Lorentz structures. They contain neutrino-quark non-standard interactions as a
subset, but span over a larger set that involves effective scalar,
pseudoscalar, axial and tensor operators. Using recent COHERENT data, we derive
constraints on the corresponding couplings by considering scalar, vector and
tensor quark currents and assuming no lepton flavor dependence. We allow for
mixed neutrino-quark Lorentz couplings and consider two types of scenarios in
which: (i) one interaction at the nuclear level is present at a time, (ii) two
interactions are simultaneously present. For scenarios (i) our findings show
that scalar interactions are the most severely constrained, in particular for
pseudoscalar-scalar neutrino-quark couplings. In contrast, tensor and
non-standard vector interactions still enable for sizable effective parameters.
We find as well that an extra vector interaction improves the data fit when
compared with the result derived assuming only the standard model contribution.
In scenarios (ii) the presence of two interactions relaxes the bounds and opens
regions in parameter space that are otherwise closed, with the effect being
more pronounced in the scalar-vector and scalar-tensor cases. We point out that
barring the vector case, our results represent the most stringent bounds on
effective neutrino-quark generalized interactions for mediator masses of order
$\sim 1\,$GeV. They hold as well for larger mediator masses, case in which they
should be compared with limits from neutrino deep-inelastic scattering data.
