The SQ website verbiage seems to imply that stopovers are only permitted on a round trip or standard award. But I was able to book a SIN stopover recently for a one way saver award (MAA-SIN-HAN) by paying an additional US$100 fee (so maybe what the website means is "complimentary stopovers"?).
You need to call to book such an award, but be sure to ask for the 15% miles discount to be honored since the (woefully inadequate) SQ website can't do it. Additionally, they might only allow this for one-way saver awards ticketed entirely on SQ metal (i.e. not a *A partner or mixed redemption) - check with KF services.