Specifically, did Muslims coin it or non-Muslims?
Is there any evidence, recorded in history, about the first usage of this term?
History Stack Exchange is a question and answer site for historians and history buffs. It only takes a minute to sign up.Sign up to join this community
No one "coined" it; it is a romanization of the genitive form of Muhammad ibn Abd al-Wahhab. The -i suffix is the usual way to transliterate it, just as we have Saudi, Kuwaiti, Omani, and so on. (The more common way in English to create a genitive for a thinker would be to use the Greek-derived -ic or the Latin-derived -an, hence you do see Wahhabic and Wahhabian like Platonic and Aristotelian).
Its first use in English is attested in various dictionaries to the first decade of the 19th century.
As an addendum to Choster's answer, Here is the English usage of "Wahhabi", according to Google's book data: