We report a synchronously-pumped femtosecond diamond Raman laser operating with a tunable second-Stokes output. Pumped using a mode-locked Ti:sapphire laser at 840-910 nm with a duration of 165 fs, the second-Stokes wavelength was tuneable from 1082 - 1200 nm with sub-picosecond duration. Our results demonstrate potential for cascaded Raman conversion to extend the wavelength coverage of standard laser sources to new regions.