"None" can be used with either a singular or a plural verb. (Ok, you might have meant 'This "none" is singular ...' , but at the moment '"None" is singular ...' comes across to me as the general statement which is a known misconception, which is worth highlighting by a couple of sourced quotes.)

"A common misconception is that none is always singular because it is short for no one. However, it is just as likely to mean not any, implying a plural." -- http://www.onlinegrammar.com.au/top-10-grammar-myths-none-always-takes-a-singular-verb/

"It is sometimes held that none can only take a singular verb, never a plural verb: none of them is coming tonight rather than none of them are coming tonight. There is little justification, historical or grammatical, for this view. None is descended from Old English nān meaning ‘not one’ and has been used for around a thousand years with both a singular and a plural verb, depending on the context and the emphasis needed." -- http://www.oxforddictionaries.com/definition/english/none

Though, that said, you could be right to highlight the plurality as the reason "None are ..." might not be accepted by the course contributors, because the German version is singular. However, another comment states "None is ..." is also not being accepted.

I suppose it is possible that when the course contributors review this, they think there is ambiguity with "none". For (a faintly ludicrous) example: I have seven nails to hold a shelf to a wall. (You can tell I'm a bad DIYer, right?) I ask, "I don't want to use all my nails. Should I use two? three?"

"None is stronger," says the person I asked, and instead hands me a tube of No More Nails.

(It's probably something else.)

Are you sure 'none' is singular? How about 'none of you are coming?' That's is sounds correct to me. But I may be wrong....

I think your explanation is excellent, especially your example of kein, which shows an example where kein is a much better candidate than its synonym.

Of course, though, the question still remains as to why niemand wasn’t accepted for this specific translation of “no one is stronger”, where either one should be fine...

5 months later and I still got rejected on "none is stronger." Wouldn't this be the answer if you are in a store looking at tape or glue and ask if a certain one is strongest?

I believe "keiner" here is simply nominative masculine singular, with kein- being used as an indefinite pronoun (rather than an article), which is why it takes the -er ending. The implied situation is one in which, for instance, you have two men. The question is asked, Welcher Mann ist staerker? (Which man is stronger?) Possible answers include:

Kein Mann ist staerker. (Kein is an article used in the nominative masculine singular, thus no ending.) In English, more or less "Neither man is stronger."

Keiner ist staerker. (KeinER is now a pronoun, replacing the noun, thus the ending). "Neither is stronger."

KeinER might also be used in this sort of sentence if the antecedents aren't clear, or if the antecedents are mixed in grammatical gender...but I'm less sure about that.

If the implied situation were different, if you were clearly looking at two women (Frau - feminine gender on the noun) or feminine gender nouns and asking which is stronger, I believe you could answer

Keine ist staerker.