Trying to visualise a balcony hand rail but could you adapt an ordinary wall basket that has a flat back?-perhaps a photo of the spot would help ??
I have some saddle planters on my balcony, the cheapest place to buy them is ebay.
If hanging planters from a balcony be mindful if there are people living below. A planter with holes in the bottom is going to drip water when watered on a daily basis, particularly during the summer if you are growing tumbling toms.
Purchasing a planter without bottom holes but with a reservoir for water is advisable so if you do have neighbours living below this won't drip.
Ebay currently have some metal balcony planters which hook over the rail, not sure how secure they would be on a windy day though.
Check out website www.hanginggardenuk.com
They sell planters made to order, sounds perfect.