Banister coming out from plaster wall, no studs
start at the most likely place there would be a stud ( ie corner of wall) and measure out 16"- if its an older house there is no promise you will have studs at the current increments- so take a small nail and do test holes to the left/right of the 16" - use small nail so you can patch test holes easily- find the stud "pattern"
I've never had success securing a railing without using the studs. As others will tell you there really almost has to be studs and should be approx every 16" starting from the nearest corner (Measuring parallel to the floor, not the diagonal of the railing).
Personally, when in doubt, I would use the old-time method of drilling small pilot holes (in the "neighborhood" of 16") until you find them otherwise the weight of persons using the railing will almost certainly pull loose almost any anchor you might use.
There has been times where I've mounted a 1x4 on the wall hitting all the studs and then been able to mount my handrail brackets equidistant,in fact ,I added additional brackets to really beef it up.
You guys were right, we found the stud! It was 14" from the corner. Thanks everyone!
Anyone have suggestions for how best to re-mount a railing into a plaster wall? Stud finder cannot locate studs. Is there a special anchor that can be used? Thanks