i live on the 3rd floor and had the same issue. i got some really thin board and had it cut in half lengthwise so it's about 12-15" high i think, i nailed mine in since it is wood out there and that makes me feel secure letting princess out there. but since you can't nail i wonder if you could cut some lattice the same way and kind of tie it to the posts? i would worry about chicken wire, it just seems like they could get caught up in it or something. but of course the lattice wont work if they're climbers either. good luck.
