Gulfair takes non rated pilots only at the moment (i.e. in the last few years).
Other A320 operators:
Saudi Arabia: NAS and it's LCC Al-Khayala, NetJets for NAS
Kuwait: Kuwait Air
Other operators:
UAE: Etihad accepts your application with A320 hours
Contractors:
The usual contractors are looking for A320 pilots for Qatar, NAS and others.
hth
Dani