What kind of door mat is it? Rubber or is more of a rug? If it is more of a rug, add a fabric medium into your latex wall paint. Try liquitex fabric medium or ceramcoat textile medium. Just google these 2 products and follow the directions on the bottle to mix with paint. I haven't done this yet so I don't have one of my own posts for you but I have thought about doing it myself and I would use these products. If it is rubber, I would not use latex paint!