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The most famous American Cokie, the reporter Cokie Roberts, was born Mary Martha Corinne Morrison Boggs. Her parents wanted to call her "Corinne", and "Cokie" was a nickname created by her older brother Tommy because he found "Corinne" too difficult to say. A great many people have pet names that were created in the same way when slightly older siblings could not pronounce their names correctly when they were small children.

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http://books.google.com/books?id=Jds8Oc1Oqt0C&pg=PA321&lpg=PA321&dq=cokie+roberts+nickname&source=web&ots=kl7D9XCzQt&sig=TzkPCSOoHppxLcWSanBf9jdwrUM

Cokkie is a Dutch pet form of Cornelia. Maybe Cokie is an alternate spelling.