Mounting Screws in Stucco
For stucco I would consider using plastic expansion anchors. For a smallish screw these should work well and minimize the size of hole you have to drill into the stucco. 

You have to be rather careful when drilling in stucco in that it is rather easy to find your hole getting larger diameter than you want. This happens when the carbide cutting tips on the masonry drill hit the wire embedded in the stucco. The stucco material is rather soft and the drill bit likes to walk to the side instead of going through the wire. 

Plastic anchors use regular pan head type sheet metal style screws. This can be an advantage if you need to re-work a mount point at some point. Using a masonry specific type of screw tends to be a one shot deal and they also require a drill hole with very close tolerances (review comment above regarding the wire in stucco).