The configuration-interaction method is applied to the study of positronic zinc (e+Zn) and positronic cadmium (e+Cd). The estimated binding energies and annihilation rates were 0.00373 hartree and 0.42×109 sec-1 for e+Zn and 0.006 10 hartree and 0.56×109 sec-1 for e+Cd. The low-energy elastic cross section and Zeff were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive (14.5a0 for Zn and 11.6a0 for Cd) the differential cross sections are larger at backward angles than at forward angles just above threshold. The possibilities of measuring differential cross sections to confirm positron binding to these atoms is discussed.