We present a calculation for coherent pion production on the deuteron in which rescattering corrections are included to all orders. These rescattering contributions are computed by solving the Faddeev equations for the πNN system. The corrections turn out to be fairly unimportant in the numerical description of the cross section in the resonance region. However, the inclusion of rescattering in the multipoles for pion production on a single nucleon has a large effect on the cross section for pion production on the deuteron. We also study the effect of the neutron contribution on the observables for pion production on the deuteron.