The hybridization should be dsp².

The Cu atom is in form of Cu⁺² in the compound. In Cu⁺², the electronic configuration would be

1s²2s²2p⁶3s²3p⁶3d⁹4s⁰

So, there would be a rearrangement of electrons in Cu²⁺ because of the NH₃​ ligand (which is a strong one). And the last electron in the d-orbital would be out waiting for the N's electrons to fill up first.