The HamStick dipole has already been mentioned.
Another HamStick or mobile antenna option is to use a single antenna with as
many ground radials running along the railing and the balcony floor as
possible. Some of these won't be resonant anywhere in particular, but that's
okay.
I did this briefly with an old hustler mobile antenna at the same apartment
where I ran the wire I described previously.
On 40 and 20 meters, the wire worked much better.
Mike Duke, K5XU
American Council of Blind Radio Amateurs