  The exciting possibility of detecting supernova, solar, and atmospheric
neutrinos with coherent neutrino-nucleus scattering detectors is within reach,
opening up new avenues to probe New Physics. We explore the possibility of
constraining non-standard coherent neutrino-nucleus scattering through
astrophysical neutrinos. Sensitivity bounds on the mass and coupling of the new
mediator are obtained by inspecting the modifications induced by the new
interaction on the recoil rate observable in the upcoming RES-NOVA and DARWIN
facilities. Under the assumption of optimal background tagging, the detection
of neutrinos from a galactic supernova burst, or one-year exposure to solar and
atmospheric neutrinos, will place the most stringent bounds for mediator
couplings $g \gtrsim 10^{-5}$ and mediator masses between 1 and 100 MeV. A
similar, but slightly improved, potential to COHERENT will be provided for
larger mediator masses. In particular, RES-NOVA and DARWIN may potentially
provide one order of magnitude tighter constraints than XENON1T on the mediator
coupling. Non-standard coherent neutrino-nucleus scattering may also force
neutrinos to be trapped in the supernova core; this argument allows to probe
the region of the parameter space with $g \gtrsim 10^{-4}$, which is currently
excluded by other coherent neutrino-nucleus scattering facilities or other
astrophysical and terrestrial constraints.
