We report ultrafast spectroscopic measurements of intersite charge transfer in a single crystal of the hydrogen-bonded material quinhydrone showing anticorrelated dynamics of vibrational coherences at 172 and $216\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. To explain these coherent dynamics we derive a density matrix model in the presence of higher order electron-vibration coupling. Given the symmetry of vibrations calculated using density functional theory, the Huang-Rhys parameter of the Raman-active vibration found from spontaneous resonance light scattering measurements, and previously reported nonresonant impulsive stimulated Raman scattering measurements on quinhydrone, we restrict the density matrix model to three levels in the excited state of this material to simulate the observed dynamics with a density matrix approach. The close agreement between the experiment and our theoretical treatment leads us to conclude that the measured behavior corresponds to intermolecular Rabi-like oscillatory coherence transfer. These results provide foundational knowledge into the capability of functional organic materials to support quantum coherent transport of charge and energy as well as shed light on recent experimental and theoretical investigations of room temperature organic ferroelectrics.