We investigate the acousto-electric transport induced by surface acoustic waves (SAWs) in epitaxial graphene (EG) coated by a MgO/ZnO film. The deposition of a thin MgO layer protects the EG during the sputtering of a piezoelectric ZnO film for the efficient generation of SAWs. We demonstrate by Raman and electric measurements that the coating does not harm the EG structural and electronic properties. We report the generation of two SAW modes with frequencies around 2 GHz. For both modes, we measure acousto-electric currents in EG devices placed in the SAW propagation path. The currents increase linearly with the SAW power, reaching values up to almost two orders of magnitude higher than in previous reports for acousto-electric transport in EG on SiC. Our results agree with the predictions from the classical relaxation model of the interaction between SAWs and a two dimensional electron gas.