It's possible to get business class on SQ going to DPS through SIN (I did it at T-330), but 2 might be tricky.

My strategy would be to try to get two premium class seats to SIN any way I could, and then get two seats on SIN-DPS, even if one or both of them were in Y (coach). It's a 2+ hour flight. You won't die sitting in coach seats for that long a flight (and from all reports SQ Y is roomier than most American carrier Y).

I would also consider what Guy Betsy suggests: connect in BKK instead and fly TG. TG has considerably better availability on their BKK-DPS flights (in fact, that's how I am returning, through BKK. SQ didn't have availability).

I've found SQ has decent award availability through HKG if your heart is set on flying part of the trip with SQ (and it makes for a reasonable connection point). Alternately, get to NRT/ICN/PVG/PEK on UA and connect to SIN/BKK there using another carrier.

Another possibility is buying a cheap flight out of SIN (or even KUL or CGK) to DPS.

One other possibility: have UA get you to SIN, and use QR (Qatar Airways) to get you to DPS (they fly that segment and I believe they are an award partner for UA, and though I don't think you can mix and match non-UA carriers and QR, I think you CAN mix UA and QR on an award, though I'd check in the UA forum).

What are your dates? There is a tool (search FT for "ANA tool") that can check *A inventory for you (so you're not calling UA over and over again).