I have seen tutorials all over the internet about how to paint coffee mugs, plates, etc with Sharpies.
Full disclosure – I have not tried it myself. This is because I have also seen sites that claim they tried it and the idea failed miserably! Within a couple washings, even if washed by hand, these people state that the Sharpie just smears right off. I decided not to attempt something that is a possible waste of resources, not to mention time, and try to find another way to do this.
The idea above shows drawing on the mug Not with a Sharpie pen, but instead a porcelain marker. These markers work just like Sharpies, but are meant specifically for ceramic, porcelain, glass and metal. After drawing, you will need to bake the mug, allow to cool and hand washing is recommended.
You can find porcelain markers at several retailers. I found one that I am excited to use (shown above) from a brand called Pebeo on Dick Blick.com art supply. They have a pretty good selection of colors and come in fine and broad widths for under $5 each. Instructions are on the link under Description.