Answer by
trudie1962 (1022)
Craft stores have paints that are specifically designed for painting mugs and plates. Some have to be heat-set (i. e. baked in your oven), others air-dry. Handwashing is often recommended for the finished product. Or go to a paint-it-yourself ceramics store, paint your mug there and have the store glaze & finish the piece in its kiln.