Using the atomic-sphere approximation formulation of the Korringa-Kohn-Rostoker coherent potential approximation (KKR CPA) method, we have studied the effects of relativity on the electronic structure of ordered and substitutionally disordered Ni-Pt alloys. The inclusion of mass-velocity and Darwin terms are found to be essential for describing the experimentally observed ground-state properties. For the stability of disordered Ni-Pt alloys we find that, in addition to relativity, the minimization of charge-transfer effects are important. We also find that the treatment of ordering tendencies based on the band energy term alone is not sufficiently accurate for alloys with charge-transfer effects. Further analysis, in terms of basis functions, densities of states and non-spherically averaged charge densities, indicate the importance ofs- andd-electrons of Pt for the stability of both ordered and disordered Ni-Pt alloys.