I'd use straw. Pine and cedar are dangerous...I just wouldn't take the risk, and it would probably affect my allergies anyways.
Or maybe you could use some sort of horse bedding? Not sure what they are made of... Aspen shavings are good but they can be a lot more expensive than pine.
Each time I clean the pen for the adults I put down a layer of shavings- then hay or straw on top. The shavings underneath make it much easier to clean as straw on its own sticks to the floor with all the poop. Shavings will absorb moisture- but dont tend to stick so much - in some places I can actually just roll the top layer of hay off the shavings- turn the shavings with a shovel or rake abit and its still good to be used a while longer.