As long as the pine is kiln dried, like what Larry has, its fine. All the phenols have been cooked out during the drying process.
I would avoid towels too, unless you know your rabbit isn't a chewer. Instead, I would look for fleece. It has shorter strands and they pass more easily through the rabbit system than towel fibers do, because towel fibers are longer. So fleece is a more safe choice. I get little cheap fleece baby blankets for Ellie for like $2 each at walmart. Or you could see if there is a fabric place near you that sells it cheaper by the yard.
Ellie also has a few velvet blankets that go under her litter box for when she pees over the side. The velvet absorbs the pee but it doesn't soak through to my hardwood floor underneath, the velvet just holds it. They're great! But I'm not sure of how safe it is, but she doesn't chew it.
But in the rest of her enclosure, she doesn't have anything. She likes to lay on the hard floor because its cooler.
I also use pine pellets as litter, they're great. And pretty cheap and so worth it. Ellie never lays in her litter box, but she does sit in it a lot to eat hay.
I think most rabbits eat where the poop, whether you put the hay IN the box or put the hay ABOVE the box, there will probably always be hay in your litter boxes and they'll eat it. They also eat their own poop, so pooping where they eat isn't as much of a big deal with rabbits.