Ni is ferromagnetic. Cu is not. When Cu is added to Ni, they form an isomorphous substitutional alloy. Some of the Ni atoms are replaced by Cu atoms.
To put it simpistically, the interaction between a Ni-atom and a Cu-atom is not a ferromagnetic interaction. For a ferromagnetic interaction between 2 atoms, you must have the right extent of orbital overlap - and this depends on the shape of the valence wavefunctions as well as the separation between atoms. In a substitutional alloy, you are not changing the interatomic spacing, but by changing the atoms, you are changing the valence orbital shapes/sizes. By making some of the near-neighbor interactions be paramagnetic instead of ferromagnetic, you are reducing the magnetization.