I'm just a housewife, not an expert, but here is how I have patched my stucco. Use regular wood exterior sheeting to fill the hole. Attach two layers of 30# roofing felt. The one closest to the wood helps keep the wood dry, the second layer needs to be wetted down when you apply the stucco and is crucial in getting the stucco to cure properly. Over the felt attach galvanized self-furringt lath with fasteners no more than 12" on center.

I'm assuming you have the same stucco recipe as mine. For the scratch coat use 1 part portland cement, 1 part hydrated lime and 2.5 to 4 parts sand. For the next, brown coat use 1 part portland, 1 part lime and 3.5 to 5 parts sand. For the finish coat use 1 part portland, 1 part lime to 1.5 to 3 parts sand. The finish coat is pretty thin and more just to texture the finish to match the rest of you stucco. I use a wallpaper brush to scratch up the first and second coats. Make sure you really wet down the surface before you apply each stucco layer and to keep it misted so it doesn't dry out too fast.

If you are trying to match the exterior texture I would make a practice board and try some different techniques.

Some old stucco's have pebbles in them but I could never find any small enough to match mine (mine has more of a mica in it). Those were thrown onto the finish coat and pressed in with a broom. When we put on our dormer I just textured with a sponge and broom since it was pretty far away from the older stucco. When we moved the four windows for the kitchen remodel it was on a newer (60 year old) addition and there were no pepples added. I used an sponge to texture the top coat and then loaded up a wisk broom with stucco and slung it at the wall for texture. It worked well.
If your stucco is unpainted you can try to match the color by adding pigment but you need to do a tester board for this and to allow up to 60 days for the color to cure. If you are matching a painted stucco then prime the new stucco twice (after curing) and then paint the patch. Then paint the whole wall of the patch if possible. New stucco absorbs a lot of paint and if you don't get a few layers on the stucco will look different that the rest of the wall.

DO NOT use house wrap (or stucco wrap) under the stucco. It will not dry out properly and it will lead to problems down the road.

The Portland Cement Association has some stucco tips on their website and you should read those. I would also recommend that you verify what kind of stucco you currently have. You will have a failure in your patch if the composition is different than the existing siding. The site listed below should help with that.

Here is a link that might be useful: how to figure out your stucco base.