Efficient, low noise conversion between different colors of light is a necessary tool for interfacing quantum optical technologies that have different operating wavelengths. Optomechanically mediated wavelength conversion and amplification is a potential method for realizing this technology, and is demonstrated here in microdisks fabricated from single crystal diamond--a material that can host a wide range of quantum emitters. Frequency up--conversion is demonstrated with internal conversion efficiency of $sim$45% using both narrow and broadband probe fields, and optomechanical frequency conversion with amplification is demonstrated in the optical regime for the first time.