Applying exterior insulation to old block house

I want to insulate the exterior of a 1950s block house in a hot, dry climate.

I am thinking of Rockwool insulation board, because of its low embodied energy, compared to polyisocyanurate.  It is also cheaper these days, and is water proof.

Do I need a vapor barrier, if I cover the insulation with stucco, which "breathes"?

Thanks, Tres

i helped a friend install these on the outside of his tiny house. We built a frame around it the thickness of the boards/batts. We than put the boards/batts onto the wall with a few long nails. We than covered that with some 1x8 pieces of wood. The boards/batts went directly onto the exterior tar paper/housewrap.

Rockwool.com says

 
   Can be easily cut with a bread knife
   Non-combustible with a melting point of approximately 1177°C  (2150°F)
   Excellent sound absorbency
   Vapor permeable
   Does not rot or promote the growth of fungi or mildew
   Low moisture sorption
   Chemically inert; non-corrosive
   Water-repellent
   CFC- and HCFC-free product and process
   Made from natural & recycled materials
   ROCKWOOL® can contribute to earning LEED® points

Hi Tres and welcome to permies! I seriously considered doing this when I lived in Tucson, in a concrete block house that was a passive solar nightmare. If we had stayed, I was leaning toward aircrete at the time, but I also liked the idea of a layer of slipstraw with a lime plaster exterior.

Rockwool sounds to me like a really good way to do this, especially since it's not going to offgas toxins. You could stucco or plaster over it with a mesh to hold everything together. A vapour-permeable water barrier would probably be necessary to keep the insulation from absorbing moisture when the stucco is saturated from driving rain (and I hope you get some of that soon).

I would suggest installing a safari style wall panel after you finish the works.
I use coloured corrugated iron and insulate it with an air gap between the finished works and this new panel.
The function it serves is to shade the wall and allow air to circulate between the panels and assist in removing the suns heat which normally would be radiated onto the wall.