Measure the width of the baluster with a tape measure. Set a table saw fence and rip the baluster lengthwise into two equal halves.
Fold a piece of 180-grit sandpaper into thirds and lightly sand the edges of the baluster to remove any light curls of polyurethane. Smooth the edge but do not round it.
Stand the baluster half in place on the column. Center it on the column and place a level vertically along one side. Make a light pencil mark on both sides of the column to indicate where the baluster it is to be attached.
Clip the head off of a finish nail with diagonal pliers. Insert it into a cordless gun to use as a drill bit. Drill one hole at each end of the baluster centered 3/4-inch from the top and bottom.
Turn the baluster over. Run a heavy bead of construction adhesive on the back of the baluster. Use a flat stick to smear it to within 1/4-inch of the edges around the perimeter of the baluster.
Stand the baluster in place using the pencil marks. Insert 3-inch finish nails in the holes. Stand the level vertically along the side of the baluster. Check the vertical alignment and then hammer the nails in until the baluster is tight against the column. Allow 24 hours for the glue to bond the baluster to the column.
Tap the nail heads below the surface of the baluster with a nail set and hammer. Putty the holes with a putty stick. Paint polyurethane balusters and stair parts just as you would wood.