Replace Banister Rod?
The simplest way to insert the new spindle is to make sure the hole in the bottom of the handrail is deep enough that the new spindle can be inserted higher than its final position, high enough to allow the bottom stub of the spindle to clear the hole in the step and then be lowered into the hole.

Once you have sized the spindle and tested it for fit, remove it, place some glue in the upper and lower holes, and reinsert the spindle, You should then pin it to the stairs with a finish nail in a 45 degree angle, then fill the nail hole with wood filler or caulk.