What window treatments do you use on your windows ie curtains etc? There are several kinds of blinds on the market now that will allow the room to still retain light but not glaring hot sun and there is also the option of putting static cling tinted window film on windows to cut down on the amt of light and heat that is emitted into a room that you can get for about 25 dollars usually at stores (its static cling so it isnt perm put on the windows and can be easily removed).
I am guessing your air conditioning isnt central air and is a box type unit so it would def be difficult to maintain coolness in that room but you might want to keep the window cracked to keep the room at least ventilated?
Make sure your birds are also out of direct sunlight and they have plenty of water. A fan might help to move air around the room but I wouldnt put it directly on them.
Most birds are able to handle hot weather as long as they have some shade and water.
good luck