We present a design methodology and analysis of a cavity optomechanical system in which a localized GHz frequency mechanical mode of a nanobeam resonator is evanescently coupled to a high quality factor (Q > 106) optical mode of a separate nanobeam optical cavity. Using separate nanobeams provides flexibility, enabling the independent design and optimization of the optics and mechanics of the system. In addition, the small gap (≈25 nm) between the two resonators gives rise to a slot mode effect that enables a large zero-point optomechanical coupling strength to be achieved, with g/2π > 300 kHz in a Si3N4 system at 980 nm and g/2π ≈ 900 kHz in a Si system at 1550 nm. The fact that large coupling strengths to GHz mechanical oscillators can be achieved in Si3N4 is important, as this material has a broad optical transparency window, which allows operation throughout the visible and near-infrared. As an application of this platform, we consider wide-band optical frequency conversion between 1300 nm and 980 nm, using two optical nanobeam cavities coupled on either side to the breathing mode of a mechanical nanobeam resonator.