This is the second part of a report on spin-free relativistic no-pair ab initio core model potentials for the transition elements Sc to Hg. In the first part [J. Chem. Phys. 110, 3678 (1999)], we introduced the no-pair ab initio model potential method and supplied model potentials for [Mg], [Zn], and [Cd,4f] cores of first-, second-, and third-row transition metals, respectively. At the Hartree-Fock level excellent agreement between all-electron and model potential results was observed for late transition metal oxides, whereas the performance of the model potentials was slightly less satisfactory for early transition metal oxides. In this paper we will present small-core model potentials corresponding to [Ne], [Ar,3d], and [Kr,4d,4f] cores, respectively. The performance of the model potentials is tested extensively in calculations on the diatomic oxides VO, NbO, TaO, NiO, PdO, and PtO, both at the Hartree-Fock level and when electron correlation is included by means of coupled-pair functional methods. Further we investigate the requirements on valence and intermediate basis sets used to represent the exchange and no-pair operators.