The quasifree pn-->dvarphi reaction has been studied at the Cooler Synchrotron COSY-Jülich, using the internal proton beam incident on a deuterium cluster-jet target and detecting a fast deuteron in coincidence with the K+K- decay of the varphi meson. The energy dependence of the total and differential cross sections are extracted for excess energies up to 80 MeV by determining the Fermi momentum of the target neutron on an event-by-event basis. Though these cross sections are consistent with s-wave production, the kaon angular distributions show the presence of p waves at quite a low energy. Production on the neutron is found to be stronger than on the proton but not by as much as for the eta meson.