I had to organise the rental of a mobile phone for one of our managers on a recent business trip and found a number of companies on the internet. I ended up using
www.rentexpress.com (new name Roadpost).
There was no deposit to pay and the rental was charged to a credit card. The phone was waiting for him on arrival at the airport terminal and he was given a pre-paid courier box to return it in. The rental charge appeared on his next credit card statement and the call charges the following month. He said the system worked really smoothly and would definitely do it again.
Another company that I looked at using was
www.rentcell.com.
Hope this helps.
Maria