Knowledge of the neutron light-yield response is crucial to the understanding of scintillator-based neutron detectors. In this work, neutrons from 2–6 MeV have been used to study the scintillation light-yield response of the liquid scintillators NE 213A, EJ 305, EJ 331 and EJ 321P using event-by-event waveform digitization. Energy calibration was performed using a GEANT4 model to locate the edge positions of the Compton distributions produced by gamma-ray sources. The simulated light yield for neutrons from a PuBe source was compared to measured recoil proton distributions, where neutron energy was selected by time-of-flight. This resulted in an energy-dependent Birks parameterization to characterize the non-linear response to the lower energy neutrons. The NE 213A and EJ 305 results agree very well with existing data and are reproduced nicely by the simulation. New results for EJ 331 and EJ 321P, where the simulation also reproduces the data well, are presented.