things like curry plant, most sedums, and sweet potato vines are pretty much immune, as long as you water them- and a window box full of purple sweet potato vine is a glorious site- not to mention that one start will fill a box, and cascade down the sides with very little help (when the main stem is as long as the box, lay it out full length, staple it down, and add a bit of mulch to cover the stem. it will root and branch out from every node, making a monster of a plant)

trumpet vine is an interesting container plant- and safer, since it's really invasive if left loose in the dirt. it will climb the brick wall (stop it before it hits the power or phone lines) and you can train it to follow twine tied to the balcony, to the point of making a nice awning.

other than that- anything that specifies 'drought tolerant (portculas, nasturtiums) will be fine.

Try using "moisture crystals" or a container mix that has the crystals included. I know that Fafard makes one.

And as mentioned, use drought resistant plants...
Purslane is one among many.

Nemesia, fancy Calendulas and California poppies (in the new shades like red and white) all handle sun and drought well and are pretty. Do use the moisture crystals though.

I, too, wanted windows boxes on my south-facing deck. I finally bought the plastic window boxes that have a water reservoir in the bottom so that I only need to water every few days, even in the hottest weather. I've never seen these boxes for sale at a garden store, but they are available from garden supply catalogs. Then I plant with heat loving plants like verbena.