Any auto paint supply can mix a vinyl "dye" for you. They call it dye, but it is more like vinyl paint. White over black will take several coats, but it will work. Follow the directions closely to prepare the surface, or it will peal later. Prep is mostly about removing the old Armour All, etc.
There is also vinyl dye in a spray can, also available at most auto paint supplies...and some large parts stores. It works, just not quite as high quality as the store mixed. The key to that type is to shake the heck out of it to mix it thouroughly before you spray.
John