How do you hang a picture on stuco?

Carefully. lol

Drill a small hole, then use a picture hanger. Make sure the hole is just slightly smaller than the nail for the picture hanger.

Don't skip on drilling the hole, or you will crack the plaster/stucco.

(I assume you meant plaster/lathe instead of stucco; stucco is outside of the house and is usually made from portland cement, plaster/lathe is used inside in older houses and is... well... plaster.)