I've never seen "coöperator" spelled with a diaeresis before. Apparently it's a New Yorker house style: http://www.newyorker.com/culture/culture-desk/the-curse-of-t...
http://www.newyorker.com/culture/culture-desk/the-curse-of-t...
We do change our style from time to time. My predecessor (and the former keeper of the comma shaker) told me that she used to pester the style editor, Hobie Weekes, who had been at the magazine since 1928, to get rid of the diaeresis. She found it fussy. She said that once, in the elevator, he told her he was on the verge of changing that style and would be sending out a memo soon. And then he died.
This was in 1978. No one has had the nerve to raise the subject since.
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¹ Or should that be diæresis?
² Speaking of style guides: Ooh, look! An Oxford comma!
Besides ü?