A cr2032 has 220mAH capacity, if you run a pair of leds at 20ma thats 40ma drain, so a single cell would last 220/40=5 hours, probably acceptable for the puck, 4 leds would be half that at 2.5 hours, might be long enough.
To increase capacity and run time you could use 2 cells, wire them in parallel, or if thats impractical wire them in series, but then you'd need some circuitry to efficiently reduce the voltage to the leds, but if your going to use some led driver logic that might be easy to do.