The IC Bali definitely has private swimming pools attached to the Imperial Villas, quite nice as well - though the per night price tag is up over US$1500 a night I think. (and I don't think they'll accidently have them available for points redemption ever again! ).

The HI Phuket has a nice setup for those staying in the Busakorn Villas. It's a shared pool, but only amongst 20 or so Villa rooms. You basically open a sliding door at the back of the room and there's steps leading straight down into the pool from each room. So not 100% private, but still somewhat secluded, and two thumbs up convinience wise!