Yes, the ideas of what to safely use to cover the furniture are very welcome. Tin foil, you said? Is it safe? Has somebody said birds died from duct tape?

Actually, I got balsa wood, many thanks for the idea! I just couldn't figure out what dimensions to get and how to introduce it to them, so I got a kit that includes various pieces. Then I forced some blocks between the cage bars on the top of the cage and here they go - chewing it up! and because the block is long (I wean it WAS long), they chew on the same block sitting inside the cage! Double benefit! The only problem is when I run out of the pieces of appropriate for between the bars dimensions, I will have to buy more. But at least I found out what sizes to get. Blocks that tightly fit between the cage bars and about 5-7 inches long.

I discovered that my birds wouldn't chew any provided cardboard. I guess some is too thick for them.
Cabob is OK but not crazy about it. Maybe because I don't have it hung up vertically, I tied it flat on top of the cage.

Since I am a really cheeky mom, when I don't want them to chew a piece of furniture where they usually land on, I cover it with brown paper (newspaper works too but looks really ugly).
Now, the trick is to have the paper a few inches larger than the furniture. They try to land on it, there is nothing underneath to sustain their weight and they fall hahhah I am so nasty!
They don't really fall of course, just fly away, and learn not to trust that surface.

That makes a lot of sense, Barbara!

Looks like I'm not the only one who thinks it's funny when birds are confounded.

When Jaid falls on his face I laugh at him. He's a dork and deserves it.