I had always assumed that someone at Disney had coined the term "Imagineering," until I came across an article from the May 2, 1947 Portsmouth Times (Portsmouth, Ohio) titled, "Black Light Magic." The article describes the work of Arthur C. Radebaugh and the caption to the picture above uses the term "Imagineering."
The Wikipedia entry for Imagineering claims that the term was coined by Richard F. Sailer in a 1957 article, ten years after this article appeared. An excerpt of the Wikipedia entry appears below:
The term "Imagineering" is a portmanteau word that combines "imagination" and "engineering." The term was coined by Richard F. Sailer in an in-house article written for the National Carbon Company Management Magazine, and reprinted by the Union Carbide Company. The article "BRAINSTORMING IS IMAGINation enginEERING" was published and copyrighted in 1957, and gravitated to Disney by unknown means. WED Enterprises applied for a trademark for the term in 1967, claiming first use in 1962.
After doing some further research the earliest mention of the word I was able to find was in an Alabama newspaper from 1942. The image below is from the 1947 Portsmouth Times article about Radebaugh.