It's pretty large and heavy- won't your cousin have problems bringing one from Italy? However, if you are looking for secondhand/used, and that's not a problem, you could try searching
www.ebay.it and having it delivered to your cousin if he's in Italy long enough at a fixed address.However, bizarrely,at present the only ones listed on ebay italy are new and from the UK!! (I search ebay italy a lot for bits for my Ritmo/Strada Abarth!)
I'm surprised you can't get one in Singapore- surely a main FIAT dealer can order you one,if you are prepared to pay full price? If not,have you tried Peugeot and Citroen dealerships, as the item for the Qubo is identical to that for the Bipper and Nemo?
Failing all else,
this one is available from UK,and they will ship internationally- though they quote only for Japan in the far East,I'm sure you'd get a similar price to Singapore?
Via ebay.sg
this one is listed as mailed to Sg from UK.(ebay item number 221259358782 in case the link fails)
But it's an expensive option to buy new- I got the whole central mechanism for £25 from ebay.uk (and sourced the 3 legs/nuts/wingnut etc from Peugeot ) from a converter of Qubos etc to motability/disabled vehicles- the floor has to be altered,meaning removal of the carrier (if fitted ! - it's standard on Bipper/Nemo,but optional on Qubo).Perhaps you might find such a converter in Singapore and get lucky?
Good luck