Bed for bunny

I would like to get Sasuke a bed of some sorts in his run, so he won't have to walk around on the floor all the time. Its carpet floor, but not very thick so it's kind of hard.
He used to have a fleece-carpet under his run but then he chewed holes in it so I took it away. He also had a pillow in his old cage but he chewed it to bits.
I can't use hay as I am allergic (I feel fine as long as there's only hay in the hayrack, so don't worry, he's got feed-hay)
Any tips?

I think cavysrock had a bed for her buns...

I will try and ask her... It looked great!