I use newspaper too, and wouldn't use anything else. Most beddings are dangerous for tiels if they decide to *eat* it, and you can't exactly *see* their droppings in the litter either. You should be able to see their droppings as abnormal droppings could be a sign of illness, and you need to watch out for that. That's the main reason I prefer newspaper to litter. Its easier to handle too, but I know its hard to fold properly for round cages.

My friend's tiels had a round cage for years and they were never satisfied in it, so although they get used to it, I'm not sure they like it. Maybe you could consider getting them a new cage sometime in the future, when you're able to. I would think that could possibly be a cause of their screaming. They look very sweet from the pictures though. Have you held them at all?