We report a diamond Raman laser that is continuously-tunable across the range from 590 nm to 625 nm producing continuous wave output with up to 8 W. The system is based on an all-fiber and tunable (1020-1072 nm) Yb-doped pump laser with a spectral linewidth of 25 GHz that is Raman-shifted and frequency doubled in a cavity containing diamond and a lithium triborate second harmonic crystal. Despite the broad pump spectrum, single frequency output is obtained across the tuning range 590-615 nm. The results reveal a practical approach to obtain tunable high-power single-frequency laser in a wavelength region not well served by other laser technologies.