My little RB girl Quasar used to prefer the carpeting, presumably because she hated the litter feel on her paws. Eventually we just cut up carpet squares and put them in a separate litter box. Once we did that, she always used the litter box. She loved the feel of her paws on the carpeting while trying to cover it up.
So, old carpeting is a thought.
THe other suggestions about newspapers might work, too. There's a brand called Yesterday's News that might be helpful.
Good luck. He sounds very precious to you.
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