You mean you are expats on EP and not on PR - sorry, just being fickle about it.
When my family needed one, when we were still not PR, we went to NUH and was told it was possible to be a full paying customer and was suggested to go to Jurong Polyclinic (their Child Development Unit was there). We tried to make appointment and was successful, although we got charged the full cost (I think something like 175 per 45 min instead of just 50 for PR/SC). I'm not sure if rules have not changed, as you know a couple of years ago they decided to trim "privileges" for PR and Foreigners.
I have just checked their website, and they do have online appointment scheduler with foreigner..
http://www.nuh.com.sg/ourServices/speci ... ntUnit.htm
If that also doesn't work, fret not as there are many out there, but they do charge exhorbitant fee. We talked to one about 2 years ago, and the institution proposed a charge of 2.5K a month for twice a week sessions of 2 hrs - can't exactly remember. I found it via a website but can't exactly remember which one now - the location is in Jurong East Central 2nd floor.
Lastly you can also approach places like kits4kids or fei yue community services for a possibility of enrolling your child to their training centre.
Good luck and let me know if I can try to help more.