Unusual in modern orthography, and I have only seen it in the New Yorker house style (the diaeresis indicates that the second vowel should be pronounced separately, which is quite different to how that mark is used in a number of other languages that use the Latin alphabet, like German and Turkish). This is subjective, but it reads as a little pretentious to me as a native speaker, compared with other ways of marking it.

More usual is 'co-ordinating' or just 'coordinating' without marking the syllable break between the prefix and the root.