Engineering the coupling between fundamental quantum excitations is at the heart of quantum science and technologies. A significant case is the creation of quantum light sources in which coupling between single photons and phonons can be controlled and harnessed to enable quantum information transduction. Here, we report the creation of designer quantum emitters featuring highly tunable coupling between single photons and phonons. The quantum emitters are formed in strain-induced quantum dots created in homobilayer semiconductor WSe2. The colocalization of quantum confined interlayer excitons and THz interlayer breathing mode phonons, which directly modulate the exciton energy, leads to a uniquely strong phonon coupling to single-photon emission. The single-photon spectrum features a single-photon purity >92% and multiple phonon replicas, each heralding the creation of a phonon Fock state. Owing to the vertical dipole moment of the interlayer exciton, the phonon-photon interaction is electrically tunable in a wide range, promising to reach the strong coupling regime. Our result demonstrates a new type of solid-state quantum excitonic-optomechanical system at the atomic interface that emits flying photonic qubits coupled with stationary phonons, which could be exploited for quantum transduction and interconnection.