The magnetic anisotropy and saturation magnetization of a series of 30 x (2 angstrom Co + x angstrom Ni + 2 angstrom Co + 10 angstrom Pt) multilayers, grown in the (111) orientation, has been investigated for Ni thicknesses ranging from 2 to 56 angstrom. Vibrating sample magnetometry showed that the easy axis of the multilayers switches from perpendicular to along the film-plane above a Ni thickness of 48 angstrom. The fact that this transition takes place at a thickness much larger than for example observed for Co/Pd or Co/Pt multilayers, is because in the present multilayers the relatively low shape anisotropy of the Ni is combined with the large Co/Pt surface anisotropy. From the measurements a value for the Co/Ni surface anisotropy of (0.29+/-0.06) mJ/m2, favouring a perpendicular easy axis, is estimated. Also results on X-ray diffraction, Kerr rotation and temperature dependent magnetization experiments are presented.