Coherent anti-Stokes Raman scattering (CARS) is used to measure the amplitude, the dephasing lifetime, and parameters of optical nonlinearities of optical phonons in a synthetic diamond film. A compact CARS apparatus demonstrated in this work relies on the use of an unamplified 70 fs 340 mW Cr:forsterite laser output and photonic-crystal fibers optimized for the generation of wavelength-tunable Stokes field and the spectral compression of the probe pulse.