Something like a melamine paint might work for a time. You are not going to get a lot of mileage out of it though.
If it were me, I would do my design and have it cut out of vinyl as floor graphics or decals like retail stores do. A sign shop that does vinyl or a franchise like Fast Signs or even Kinko's should be able to help you out. At least with an applique you can replace what gets chewed up. Don't make it too frilly though or you will just have too many edges to catch walking around.