Patching large holes in stucco is a job that homeowners adept at basic home repair skills can handle—but it may be difficult to create a patch that blends perfectly with the existing wall (unless you repaint).
If you think this may be the situation in your case, contact a local siding contractor. If you decide to do the job yourself:
1) Remove loose stucco from the hole with a cold chisel and ballpeen hammer as shown below left; blow out the dust. Staple new wire mesh over any damaged mesh. Spray with water.
2) Apply the first coat of stucco to within 1/4 inch of the surface, using a mason’s trowel or putty knife (stucco should ooze from behind the mesh). When firm, scratch with a nail. Cure for two days.
3) Apply the second coat over the dampened first coat to within 1/8 inch of the surface, using a mason’s trowel or putty knife, as shown below right. Smooth the stucco and let it cure for two days.

4) Apply the final coat over the dampened second coat with a metal float or mason’s trowel. Smooth flush with the existing surface. Texture as desired; cure for four days.