Recent progress in the development of novel organic scintillators necessitates modern characterization capabilities. As the primary means of energy deposition by neutrons in these materials is n-p elastic scattering, knowledge of the proton light yield is paramount. This work establishes a new model-independent method to continuously measure proton light yield in organic scintillators over a broad energy range. Using a deuteron breakup neutron source at the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory and an array of organic scintillators, the proton light yield of EJ-301 and EJ-309, commercially available organic liquid scintillators from Eljen Technology, were measured via a double time-of-flight technique. The light yield was determined using a kinematically over-constrained system in the proton energy range of 1-20 MeV. The effect of pulse integration length on the magnitude and shape of the proton light yield relation was also explored. This work enables accurate simulation of the performance of advanced neutron detectors and supports the development of next-generation neutron imaging systems.