If you just want a catnap, the Sounds of the Rainforest booths at Rafiki's Planet Watch are air conditioned and dark -- and if you don't put on the headphones they're quiet too. (If you do put on the headphones, the experience is about 5 minutes).
Before I get flamed, I would never recommend using these booths for this purpose if there is a line of people waiting to use them, nor would I recommend an extended stay. However, frequently when I've been there (late August) they are roughly 1/3 empty at any given time. Under those conditions, I wouldn't hesitate to take a small child who needs a few moments of peace to calm down enough to fall asleep / become quite drowsy and then be placed in a stroller into one for this purpose, or to set an alarm on my iphone for 15 minutes and use it for a nap myself.