A systematic study of the radiative proton capture reaction for all stable nickel isotopes is presented. The results were obtained using 2.0-6.0 MeV protons from the 11-MV tandem Van de Graaff accelerator at the University of Notre Dame. The γ rays were detected by the NSCL-SuN detector utilizing the γ-summing technique. The results are compared to a compilation of earlier measurements and discrepancies between the previous data are resolved. The experimental results are also compared to the theoretical predictions obtained using the non-smoker and smaragd codes. Based on these comparisons an improved set of astrophysical reaction rates is proposed for the (p,γ) reactions on the stable nickel isotopes as well as for the 56Ni(p,γ)57Cu reaction.