Here are two. The first two don't have a website that I'm aware of, the rest - websites and the addresses can be found there.
Clifford Numismatic & Collectible Centre
#02-45 Peninsula Plaza, High Street, 179098, Singapore
p: 63373898,62231044,62249192 f: 63373872
Far East Stamp & Coin Centre
#04-48, High Street, 179098, Singapore
p: 63396808
http://www.taisei.com.sg/
http://www.worldcurrency.com/
The following are coin dealers - whether or not they handle notes I don't know...
http://www.eguide.com.sg/Products/Numismatists
edited so it made more sense (found some more so the initial prelude didn't read right.