You can try
The Camera Workshop
@ Peninsula Shopping Centre located near Cityhall MRT Station
The Camera Hospital
@ Sunshine Plaza located at the Bugis.
Meanwhile,
You can try looking for a used set at this forum, _ Buy & Sell
http://www.lomotionsg.com/
Do take note that looking for the Polaroid Films are aren't easy to find too, Fuji Instax is the next alternative.
Hope you enjoy your trip to Singapore, don't forget to try out our local delicacies like Laksa, Chicken Rice and Fried Carrot Cake.