How to insulate the walls in a stucco house

I assume you mean to insulate the walls. Houses of that vintage often had no insulation between the wall studs. The easiest way to insulate them without wrecking the stucco or drywall is to drill holes through one or the other at the top of the stud bay and blow in cellulose insulation.

However, when you do this, you impair the ability of the wall to dry when it gets wet, since there's less heat flow and less air flow through those empty cavities--both of which promote drying. This isn't much of a problem with a modern wall where the stucco is separated from the wood with tar paper or housewrap, but in an old house like yours, oftentimes the stucco was applied over wood lath with no tar paper separating it from the board sheathing; in fact, in many cases, there was no sheathing at all! They simply nailed wood lath to the studs and stuccoed it.

In such a wall, adding blown-in cellulose insulation can be a problem when the stucco gets wet, since it can't dry as easily, and cellulose itself is capable of storing water. The risk of this approach depends on the climate and the construction. If your house is in rainy San francisco, it's riskier than in Campbell or San Jose. If your house has no sheathing and/or no tar paper under the stucco, it's riskier than if it did.

In such borderline cases, the prudent approach, if you really want to insulate, would be to remove all the stucco, install batt insulation (fiberglass or mineral wool) between the exposed studs, then install plywood sheathing, wrap the house in tar paper or housewrap, apply 1+ inches of rigid foam or mineral wool insulation over that, then nail 1x3 furring strips over that, and then apply new stucco or siding over the furring strips. Obviously this would be the most expensive option but it would result in a very well insulated wall and have zero risk of mold or rot.