In our previous work, we have measured the neutron spallation cross sections of C-12 and Bi-209 in the 20- to 150-MeV energy range. Here in this succeeding study, the neutron activation cross sections on spallation reactions for Co-59 and Cu-nat have been measured in the quasi-monoenergetic p-Li-7 neutron fields in the 40- to 120-MeV energy range which have been established at two cyclotron facilities of Takasaki Research Establishment; of Japan Atomic Energy Research Institute (TIARA) and the Institute of Physical and Chemical Research (RIKEN). The neutron spectrum has been measured with the TOF (Time of Flight) method using an organic liquid scintillator, and the absolute value of peak neutron fluence has been determined from the proton recoil counter telescope at TIARA and the activation method of lithium target at RIKEN. In this study, the following seventeen neutron activation cross section data are reported which produce Mn-56, Mn-54, Mn-52, Co-58, Co-57, Co-56, Co-55, Fe-59 from Co-59 reactions and Mn-56, Fe-59, Co-60, Co-58, Co-57, Co-56, Cu-64, Cu-61, Cu-60 from Cu-nat reactions. Our experimental results were compared with other experimental data and the calculated results by Odano and Iwasaki using the SINCROS-II code for Co-59 reactions and by Fukahori using the ALICE-F code for Cu-nat reactions.