Single longitudinal mode (SLM) operation of a 620 nm diamond Raman laser is demonstrated in a standing-wave cavity that includes a second-harmonic generation element. Mode competition provided by the harmonic mixing is shown to greatly increase mode stability, in addition to the benefits of the spatial-hole-burning-free gain medium. Using a multi-longitudinal mode 1064 nm Nd:YAG pump laser of power 321 W and linewidth 3.3 GHz, SLM powers of 38 W at 620 nm and 11.8 W at 1240 nm were obtained. The results indicate that simple standing-wave oscillators pumped by multimode Yb or Nd pumps compose a promising practical route towards the generation of high-power SLM beams in the yellow-red part of the spectrum.