There's an art school at the esplanade for children.
If you are looking at chinese painting, you can try schools located at outram.
Oil painting and water color painting courses can be found at esplanade, local cummunity clubs (if applicable, try
www.pa.com.sg), there are also retail stores conducting specialised painting workshops on an ad hoc basis at Bras Basah Centre. Or you can engage with a private art tutor (can be found in classified ads in the Straites Times, esp on saturdays)
Hope this helps