Using the Brouwer formula, we employ Green's function technique to study charge pumping in shuttle geometry double walled carbon nanotubes. We find strong chirality dependence, and that there is virtually no pumping if the chiral angle of the two walls is the same. We discuss which are the optimal chiralities that can be used for such quantum pumps. Furthermore, we argue that charge pumping with double walled tubes can be used to probe the strength of the inter-layer coupling between the inner and outer nanotube.