We present a theoretical study of quantum charge pumping with a single ac gate applied to graphene nanoribbons and carbon nanotubes operating with low resistance contacts. By combining Floquet theory with Green's function formalism, we show that the pumped current can be tuned and enhanced by up to two orders of magnitude by an appropriate choice of device length, gate voltage intensity and driving frequency and amplitude. These results offer a promising alternative for enhancing the pumped currents in these carbon-based devices.