Phonons are envisioned as coherent intermediaries between different types of quantum systems. Engineered nanoscale devices, such as optomechanical crystals (OMCs), provide a platform to utilize phonons as quantum information carriers. Here we demonstrate OMCs in diamond designed for strong for interactions between phonons and a silicon vacancy (SiV) spin. Using optical measurements at millikelvin temperatures, we measure a line width of 13 kHz (Q-factor of ∼4.4 × 10⁵) for a 6 GHz acoustic mode, a record for diamond in the GHz frequency range and within an order of magnitude of state-of-the-art line widths for OMCs in silicon. We investigate SiV optical and spin properties in these devices and outline a path toward a coherent spin-phonon interface.