I need a better picture of what you're dealing with... but as a guess: try duct tape! just kidding. Can you drill through one part of the bannister into the other part (i.e. through the split?) If so, drill a hole that goes through the bannister (drill up from the bottom or some otherwise hidden place), also drill a counterbore. Then drive a screw through to join the two pieces (you're best off to clamp & glue first, if possible. - use a strap clamp.) Put as many screws in there as you can fit without damaging the wood. Then, fill the counterbore using a dowel rod.
..also, try to drill the holes as perpendicular to the split as possible.
If you can't do the drill/screw method, you may have to settle for the glue/steel plate method.