I don't think it is possible to stain glazed tile. You can paint floor tile but it doesn't last very well.
What I would do is sand it lightly to cut the gloss and prime it with Zinsser's Cover Stain (oil). Then paint it with oil enamel.
At that point you will have the new color but it will chip off right away. So you will need to apply several coats of floor grade latex finish. Varathane makes one called Diamond Finish. At that point it will be a bit tougher. May last a couple years before it starts looking ratty.