It helps to have a real stud finder or know how to "knock" on a wall to find the studs. Once all the studs are located, you could mount a diagonal 1x6 against the wall. I nicely finished 1x6, stained to match the rail would look good. This can be attached, preferably by screws, to the studs and then the hand rail mounting hardware mounted to it.

Now if spacing is critical here and you don't feel you can live the the extra 3/4" intrusion into the stairway, you could lay the 1x6 up against the wall where you want it positioned, then mark it ad remove the lath and plaster underneath it. That way the 1x6 would be inset into the lath and plaster wall and should only protrude by no more than 1/4". One advantage to this is that you will definitely find all the studs.