Integrating atomic quantum memories based on color centers in diamond with on-chip photonic devices would enable entanglement distribution over long distances. However, efforts towards integration have been challenging because color centers can be highly sensitive to their environment, and their properties degrade in nanofabricated structures. Here, we describe a heterogeneously integrated, on-chip, III-V diamond platform designed for neutral silicon vacancy (SiV0) centers in diamond that circumvents the need for etching the diamond substrate. Through evanescent coupling to SiV0 centers near the surface of diamond, the platform will enable Purcell enhancement of SiV0 emission and efficient frequency conversion to the telecommunication C-band. The proposed structures can be realized with readily available fabrication techniques.