I thought of this the other day, if you have the room....
get the puzzle floor mats the jumbo ones and put them out on the grass if need be then surround them in a play-yard! They are outside, free to roam in that area and wont get messy.
It may take just a few min to set up each time - I wouldn't leave the foam mats out there all day.
Hi! I actually have all my concrete patio stones covered with those large multi coloured foam mats and I leave them out all the time!! They get hosed when I wash the playhouse etc and have held up really well!!!!