How 'bout wall-to-wall carpet remnants??? Or, forget covering it at all and just let the kids have a 'mud party'. Have the parents bring a couple changes of clothes, a pair of 'aqua shoes', and away you go! You can hose them off as you need to. And you can even set up some tables and chairs out there to feed them!
Gee, other than that - Have the party at another location. My best to ya and hope this helps.