http://www.jazirahaviationclub.com/index.aspx
Try the above link.
At Dubai itself, the security regime makes it somewhat tiresome to fly in one of their Cherokees unless you are going to be there for a period of time to warrant the energy/time you'll expend trying to organise.
Jazirah Aviation is up in RAK and is a great experience that is not widely marketed. It may not be your thing and you are constrained to flying in RAK airspace. This said, being low over the gulf coastline is exhilarating and flying up in the mountains on a clear day with good vis must be akin to having wings!
It's worth a look and is totally hassle free.