If you are looking for a rug, then look for a rug with a low VOC certification.
If you want some tougher, I would suggest a natural cork or linoleum click floor laid over the slate if the slate is smooth and even. You can take it up after the kids are grown.
The CRI Green & Green Plus programs cover carpets and pads. Keep the VOC maximum to 50 g/L at most for the pad and have the carpet do an even better rating.For background on the CRI rug certification go here.
You'll be able to read about what chemicals are addressed and where to find further information.
For more information:
Read "I want to buy a rug for a baby's room that is very safe, not very expensive. What material should the rug be made of?" a Q&A answered by Jason Kliwinski.