We extend rainbow refractometry to quantify the oscillations of a droplet in its fundamental mode. The oscillation parameters (frequency and amplitude damping), extracted using the time-resolved rainbow angular shift, are utilized to measure surface tension and viscosity of the liquid. Proof-of-concept experiments on an oscillating droplet stream produced by a monodisperse droplet generator are conducted. Results show that the relative measurement errors of surface tension and viscosity are 1.5% and 8.4% for water and 5.3% and 2.5% for ethanol. This approach provides an alternative mean for characterizing liquid surface properties, e.g., dynamic surface tension and viscosity, especially for liquids with a low Ohnesorge number.