A bstract We present the constraints on the parameters of several light boson mediator models obtained from the analysis of the current data of the COHERENT CE ν NS experiment. We consider a variety of vector boson mediator models: the so-called universal, the B − L and other anomaly-free U(1)′ gauge models with direct couplings of the new vector boson with neutrinos and quarks, and the anomaly-free L e − L μ , L e − L τ , and L μ − L τ gauge models where the coupling of the new vector boson with the quarks is generated by kinetic mixing with the photon at the one-loop level. We consider also a model with a new light scalar boson mediator that is assumed, for simplicity, to have universal coupling with quarks and leptons. Since the COHERENT CE ν NS data are well-fitted with the cross section predicted by the Standard Model, the analysis of the data yields constraints for the mass and coupling of the new boson mediator that depend on the charges of quarks and neutrinos in each model under consideration. We compare these constraints with the limits obtained in other experiments and with the values that can explain the muon g − 2 anomaly in the models where the muon couples to the new boson mediator.