For Birds again the best thing is to give a grace period. Usually by the time you are hearing the babies they will soon be flying with mom. Do not disturb the birds, they can not leave until they can fly. Once you are certain they have moved on, and there is no signs of activity, you can take the nest apart. Keep and eye on the area and if you see signs of nesting materials such as twigs, you need to keep removing them before the nest is complete. Trying to keep your balcony free of clutter also helps discourage future nesting.