Optomechanical cavities are powerful tools for classical and quantum information processing that can be realized using nanophotonic structures that co-localize optical and mechanical resonances. Typically, phononic localization requires suspended devices that forbid vertical leakage of mechanical energy. Achieving this in some promising quantum photonic materials such as diamond requires non-standard nanofabrication techniques, while hindering integration with other components and exacerbating heating related challenges. As an alternative, we have developed a semiconductor-on-diamond platform that co-localizes phononic and photonic modes without requiring undercutting. We have designed an optomechanical crystal cavity that combines high optomechanical coupling with low dissipation, and we show that this platform will enable optomechanical coupling to spin qubits in the diamond substrate. These properties demonstrate the promise of this platform for realizing quantum information processing devices based on spin, phonon, and photon interactions.