Dear Student,
+2 state is the common oxidation state of transition metals.
Cu has electronic configuration : 3dā10 4s1
Cu can lose the unpaired electron present in 4s in order to attain fulfilled stability and can show +1 oxidation state also.
Zn has electronic configuration : 3d10 4s2
Now, Zn donot have +1 oxidation state. This is because, +2 state is more stable as it will lead to full filled stability.