It is possible to paint linoleum. I know cuz I saw it on the christopher lowell show. You need to make sure the floor is very clean especially if it has a waxy build up. Then you prime with a Kilz primer. This primer will adhere to any hard surface. Then apply at least 2 coats of paint to make sure you have good coverage and follow up with two or three coats of polyurethane varnish. I have never tried it but I saw it done and I plan to do this treatment in my kitchen this spring.