When a black ring starts to appear around the base of a toilet under the linoleum it generally means the wax ring that seals the toilet to the floor underneath is leaking. The color is coming from a black bacteria, mold or sewage. The only way to fix this is to pull the toilet off the floor, remove the toilet’s wax ring and replace it with a new wax ring gasket. I would also suggest making sure the drain line is cleared under the toilet – as long as you have it off the floor. If the toilet cannot flush properly, then the water will build up and put pressure on the wax ring causing it to leak. If you're not accustomed to this kind of work, you might save yourself a lot of headache by calling an experienced plumber to check for toilet leaks and to get the job done right the first time.