Translation:There are no children by the deep water.
Yes, and also the similar 'there aren't any'. Nevertheless, 'there are no' is the most elegant choice, in my opinion.
yes, though I am not sure if only the most elegant solution should be accepted in the source language :D
As a native English speaker, I have to admit that the English translation offered here seems a little unnatural. I wouldn't use 'AT the deep water' on its own. The use of 'at' leaves me wanting more detail: 'at the deep water what?'
I'd say "near" as a better translation - even if it isn't exactly what the Hungarian says. But "by" is better than "at".