Not quite perfect, but at my house, we have tile downstairs. Over the tile we have an area carpet. It's rather short. Since I'm pretty much only using bearing tips right now, it works fine. I also get a nice, big 10X12 area to throw within. I'm also mostly working on the basic throw and scoop. I'm new.
I'm looking for a decent solution for when I am out and about, mostly at parks in grassy areas, as using a frisbee is great and all, but I'd like something more substantial. I figure if I can find the right materials, I can make an 18"X18" square or circle and cover that with some carpet remnants and then glue it down using carpet glue. It's certainly not a perfect solution but it would lay rather flat on grass and with enough weight to stay fairly level but not weigh enough to crush the grass.
My suggestion for you would be similar to what I have going on at home: You can get small, low-shag, low pile area carpets if you want something nice, neat and pre-made. If everyone likes it, maybe you can just have it stay put. Otherwise, smaller is better since you want portable. Heck, a bath mat(the towel-type) can be fairly useful.
My regular carpet is too deep. Everything spins out far too quickly.