Buy 24k BMI diamond club miles on their website for $430 then for a fare $224 + tax you have 2 one-way SIN-NRT's in business class ^

For 31/12-01/01 the following are available:

1) 31/12 NH112 (763) direct. d:8:30 a:16:20 2 pax in C class tax = $69pp

2) 30/12 SQ656 (333) SIN-FUK d:01:05 a:08:00 then connect to ANA domestic

3) 31/12 many SQ flights to PVG with many ANA connections to NRT

4) 01/01 UA and SQ options to HKG connecting with ANA to NRT

All above is in business

Personally I would just put them on the direct with NH. The overall cost would be $396 each for your parents in C class ^
Not the best seat but still very nice for the day flight and NH service is top notch!!

BMI also allows you a stopover and they can be very relaxed on routing rules so if I were you I would try get the HKG-SIN flight thrown in for free in business class! PM me if you want any help!