(Updated May 2016)
While I haven’t had the chance to check if there is a nursing room at Singapore Art Museum’s main building, they do have a nursing area at their annex building, SAM at 8Q. This is the venue of Imaginarium, Singapore Art Museum’s annual event for children.
The nursing room at SAM at 8Q was located on level 2. After you go up the stairs, turn right and look for the baby changing sign and walk down the corridor.
What they had here was not really a nursing room. They converted the empty corridor to sort of a nursing area.
There are two ‘cubicle’ for nursing, separated by curtains. Within each ‘cubicle’ is a sofa and a diaper-changing table.
Not the most glam nursing room around, but better than nothing. At least they tried.