The complex ion [Cu(NH3)4]2+ has:
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
1s2,2s2,2p6,3s2,3p6,3d9,4s0
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.
[because NH3 is a strong ligand and the electrons donated from it should have got a place first--this is only punctuation]
So, the 4 electron pairs from N would be in one 3d, one 4s, & two 4p orbitals and in the third place of 4p orbital, the e− from 3d would take place. So, you can say the hybridisation here would be dsp2. Square planar with one unpaired electron.