Unfortunately there is not much you can do. Maybe try a scat mat or something, depending on where the birdcage is? The first day or two I brought my bird to my new place, the cat was jumping on the cage. After that, she hasn't done it since. Do you think she would ever realize she's not going to catch the bird, and would stop? I also have a pretty big cage for a cockatiel, it has very heavy bars and is on a stand by itself (you could probably fit 4 cockatiels in it with no problems).

What about a cage that hangs from the ceiling? Or what about rearranging furniture?