The mainstream alternative: the x-metodo
The emergence of the internet saw lots of people swapping pens and paper for keyboards, which brought the problem to the fore. These early denizens of cyberspace could've used the h-metodo but because of its potential problems chose another approach; they used the letter X as the trigger, placing it after each of the letters which required the accent:
cx = ĉ, gx = ĝ, hx = ĥ, jx = ĵ, sx = ŝ, ux = ŭ
By using a letter which wasn't part of Esperanto's own alphabet as the trigger, they removed the ambiguity which sometimes resulted from the h-metodo. The x-metodo isn't officially recognised but it is by a long shot much more common than the earlier alternative. Many Esperanto sites, including this one, assume its users will use the x-metodo and automatically change the letter to the accented version.