Does anyone write "noöne" with a diaeresis?

Whenever you find a computer spell-checking program does not know how to spell something, your best first assumption is that the program is an idiot. You will usually be right this way.

Including in this case: Wiktionary lists noöne as an “obsolete” spelling of no one.

Did people use it? Yes.

Do people use it? Yes, again!

Morover, a simple Google search would have revealed these answers and many more. One recent published example is from Roger Clarke’s English prose translation of Alexander Pushkin’s Eugene Onegin, published in 2011 under ISBN 978-1-84749-160-2:

No there is noöne else in the world I could have surrendered my heart to. It is decreed by the highest authority, it is the call of Heaven: I am yours, Eugene.

Edit

After pawing through general Google results, I really do get the feeling that the archaic noöne spelling is experiencing some strange kind of orthographic renaissance, but for what reason, I have no idea. Most of the general online results are 21^st century ones. I can’t find many from the late 20th century.

I see three groupings of letters used with diacritics in English:

1. It may simply be that people are becoming more familiar with how to use keyboard shortcuts for diacriticking words in English like Zoë, Chloë, Noël, café, coöperate, reëlect, learnèd, zoölogy, oöcyte, which are all perceived to be “native-English” words, whatever their origin.
2. Those are different from “unassimilated” imports like Ångström, Renée, José, naïve, façade, résumé, jalapeño, El Niño, Curaçao, São Paulo, Shijō, Ceaușescu, etc.
3. The restoration of diacritics to words long spelt without them in English, words like noöne, mosaïc, hôtel, rôle, châteaux, and so on, might be something else, some sord of fad perhaps. It almost seems like it might be such on Stack Exchange Chat, where noöne is strangely common.

However, I don’t see us ever going back to adding actual Ænglisc letters like æsc, eth, thorn, yogh, or wynn back into current orthography. I have seen nothing at all like this happening the way we may be seeing occur with diacritics, where people freed of the tyranny of the typewriter can once again write whatever they please.

The fiercest defender of diereses I know of in the professional world is The New Yorker magazine, which still spells it "coöperate," and even they don't spell it "noöne."