How do I install stucco over an exterior painted stone wall?
Painted stone will not provide any adhesion for the stucco, and you'll get an uneven surface.  You will need to use some masonry nails and a firing hammer and peg up some expanded steel over the stone.  Aim for where the mortar is, assuming there is some.
 Important - Stone walls are not necessarily stable items.  If this is shared with a neighbor, make sure to talk with them about it first. It would not be difficult to crack the stones, and ruin what they think is a beautiful thing.    I'd consider doing a concrete pour - Put some rebar stubs into the wall, add some fencing for extra support, and fill it up.  Great way to add in benches or other features (potting areas, fountains) at the same time.