Yes you can paint vinyl cove base but I would only do it as a last resort as now it is a maintenance issue. Befoe you paint this you will need to make sure there is not some type of film on the vinyl that will affect adhesion. You will need to wash the vinyl with amonia and water twice to sure it is clean. The primer will need to be water based and can be something like Zinnser 123 and then finish with an enmael ( oil or acrylic) because of the abuse this will get.