They seem to be much less used these days in English, but in times past you wrote "coöperate"

I am a native speaker of English and have to agree that they are not seen as much as previously. I put this down to very poor support for any sort of accents in word-processing software aimed at the English-speaking market up until maybe 10 years ago. However, I must also say that I don't recall ever seeing a diaeresis in coöperate, although plenty of times I have seen it with a hyphen to obtain the same effect, ie. "co-operate".

Some words still look strange to me when I see them unadorned such as: Noël, naïve, Zoë, etc. Perhaps that too will fade with time.