you could try the Warren Municipal Golf Club off Grove Road in Wallasey Village. Its a council run 9 hole golf course. You can pay per round or buy membership. The telephone number is 0151 639 5730, satnav code is CH45 0JA.
Alternatively try the Chip and Putt at the end of Harrison Drive, always busy with people practising shots, again it's council run, I don't know the contact number.
Hope this helps