Thanks, Karen and Bob!
I have a good friend who likes to work with wood. Since I already have some long planter boxes, perhaps he can make something for me to stabilize them on top of the railing. If not, those brackets on Bob's link might work well.
If not, just being up the one foot or so of the height of the planter box will help. I can sit on my little rolling garden stool to work with the boxes.
