I use sisal rope which is available at most hardware stores. You would know it as twine. It is made from an agave plant which is safe

It comes in various thicknesses. You can use the larger one for perches as well.

I have made bird toys in the past, but I was given a large basket of safe string from the breeder, which is long gone, and I don't remember what it was. I really need help finding something safe for my little guy :)