Though you’re better off leaving major stucco repairs to a mason or stucco specialist, you should be able to handle fixing minor holes or cracks. Repairing a hole in stucco calls for cleaning out the area and applying a new patch of stucco mixture.
To patch small holes (less than 6 inches wide), you don’t need to layer stucco as if you were applying new stucco to the house or repairing a large hole (See Stucco Siding: Repairing Large Holes. You can simply pack the hole with stucco patching compound.