I would dilute the muriatic acid with four parts water to one part acid first and then apply it with a sponge or brush, let it sit for a little bit, scrub a little and then rinse off with a garden hose. If you do try that, use googles and gloves and wear clothes you don't mind destroying.
Tile soap will also help, and isn't as much of a pain to apply. Some people mix the soap with acid and apply both at once. It might be good to try out a small area first before tackling the entire coping.