Under running water wash the cucumber well and chop it in to big chunks. If the cucumber is mature, scoop out all seeds and discard. Otherwise you can use the seeds too.
Next, in a blender take the drained rice, cucumber and grated coconut. Grind them together to fine puree adding water as needed. Transfer it in to a wide bowl.
The neer dosa batter should be very thin in consistency, so add some more water to get it right. When the batter is ready, heat a dosa griddle.
Grease the griddle with enough oil and as it is hot enough, pour the neer dosa batter so that it covers entire griddle. Pouring the batter as thin layer over the griddle is what makes neer dosa unique. Close the lid and let the dosa cook for about few seconds. As the edges of cucumber neer dosa loosen, using flat spatula carefully fold it in half and remove from griddle.
Continue the process with rest of the batter. Cucumber dosa is ready to serve with coconut chuntey and sambar of your choice.