Single-crystal diamond cavity optomechanical devices are a promising example of a hybrid quantum system: by coupling mechanical resonances to both light and electron spins, they can enable new ways for photons to control solid state qubits. However, realizing cavity optomechanical devices from high quality diamond chips has been an outstanding challenge. Here we demonstrate single-crystal diamond cavity optomechanical devices that can enable photon-phonon-spin coupling. Cavity optomechanical coupling to $2,text{GHz}$ frequency ($f_text{m}$) mechanical resonances is observed. In room temperature ambient conditions, these resonances have a record combination of low dissipation (mechanical quality factor, $Q_text{m} > 9000$) and high frequency, with $Q_text{m}cdot f_text{m} sim 1.9times10^{13}$ sufficient for room temperature single phonon coherence. The system exhibits high optical quality factor ($Q_text{o} > 10^4$) resonances at infrared and visible wavelengths, is nearly sideband resolved, and exhibits optomechanical cooperativity $Csim 3$. The devices potential for optomechanical control of diamond electron spins is demonstrated through radiation pressure excitation of mechanical self-oscillations whose 31 pm amplitude is predicted to provide 0.6 MHz coupling rates to diamond nitrogen vacancy center ground state transitions (6 Hz / phonon), and $sim10^5$ stronger coupling rates to excited state transitions.