The short answer is: Nothing, really. Backpacks really kind of suck in warm, humid weather. Ones that are waterproof are even worse.
Gregory's Jade 40 ($189) -- a women's pack that is similar to their Z45, which I've worn in hot (but dry) weather -- is one such option. It's a good long-weekend pack if you pack carefully, with 2,500 cubic inches of space. It's a top-loader, with a big pouch/pocket in pack and a largish top lid. And it's designed so the load-carrying part of the pack sort of curves away from the back, creating a bit of a wind tunnel. That works well on the Z45, as the load is not pressed against your back. I imagine the Jade 40 feels much the same.
Osprey's Aura 50 ($200) is just a touch larger, and has an all-mesh back panel that does a lot to keep your back as cool as possible. Excellent suspension, and lots of storage options for things you want close at hand.
Your best option for rain protection probably will be a pack cover. That way, you'll retain some breathability across the back while protecting your pack contents. REI's 40-liter Duck Back Rain Cover ($23) is about the right size for the packs described above. It's made from polyurethane-coated nylon for complete waterproofness.
Alternatively, simply take a large garbage sack and use it as a liner for the pack. Stuff everything in there.
Where does one buy outdoor gear in Tahiti?