Any help how to hang the railing back up on the stairway. It is townhouse wall with drywall and concrete behind it.
You can drill holes into the concrete with bits made for concrete. Depending on how dense the concrete is you can sometimes do this with a regular drill. (This takes some patience, it's not like drilling into wood. Don't push too hard or you'll break the bit. Just have patience) If the concrete is too dense, a hammer drill may be necessary. And yes they have concrete anchors. They also have special screws made for concrete that don't require anchors.
Another idea would be to put a railing on the other side. Not a hand rail. A railing that attaches to the floor instead of the wall.
i am assuming that the situation you are describing is drywall on furring strips on concrete (so there is a 3/4" or so gap between the drywall and the concrete). if its drywall directly on concrete, see the first answer. if its the latter than see below.
the issue is always with a railing the loading of the railing on the brackets causes crushing of the drywall and eventual destruction of the gypsum. if its over a stud, this is not too bad and repairable, but if over a void, then eventually the bracket punches a hole. a good tip for this is to mark out your bracket locations and then trace the actual bracket mounting flanges. in the center of the flange (not where the screws will go) drill a 1/2" hole in the drywall. mix up some unsanded tile grout into a firm but still fluid mixture an inject into the hole with a sausage gun (or a ziploc bag with a corner cut out of it in a pinch). squeeze a large amount into the hole (500ml) and leave to cure for a day. this will leave a solid cementious plug in behind the exact spot where the railing brackets will mount. then anchor your brackets as described in the above answer. now your brackets wont break through the drywall over time, and the flange of the railing bracket covers up the hole entirely so you dont see the injection port.