The optomechanical interaction between photonic and phononic waves in micron scale devices is increasingly becoming important for ultrasensitive force and mass sensing applications. Diamond is an exception material for the coupling of optical and mechanical modes because of the low absorption in visible spectrum and high mechanical modulus. To generate optomechanical coupling it is essential to achieve mechanical resonances in the GHz range. Previous work has shown that it is possible to achieve acoustic band gaps at such high frequencies by high-order band gaps which exploit periodic structures with novel topologies. In this work we investigate how the topology and geometry of the periodic structures influence the photon and phonon mode-confinement as well as the optomechanical coupling. By changing the topology and geometry of a unit cell structure based the properties of the targeted Bloch mode, both the resonant mode frequencies and the bandwidth can be tuned. The design method is able to achieve structures with quite large gap sizes for out-of-plane wave, in-plane wave, and the combined waves, which introduces more controllable mechanical modes in the cavity designs in diamond for strong coupling effects.