The Oxford English Dictionary Online (available through personal or institutional subscription) provides, as its first two quotations:
"1970 A. CHANDOR et al. Dict. Computers 254 Middleware, computer manufacturer's software which has been tailored to the particular needs of an installation."
"1972 Accountant 27 Apr. 537/2 A comparatively new term 'middleware' was introduced because, as some systems had become 'uniquely complex', standard operating systems required enhancement or modification; the programs that effected this were called 'middleware' because they came between the operating system and the application programs."
"middleware" OED Online [Oxford University Press] available by subscription at http://dictionary.oed.com
The first citation is to "A Dictionary of Computers", a/k/a "The Penguin Dictionary of Computers", edited by Anthony Chandor et al. "The Penguin Dictionary of Computers (Penguin Reference Books)"
Amazon.co.uk http://www.amazon.co.uk/exec/obidos/ASIN/014051127X/qid=1067540389/sr=1-2/ref=sr_1_0_2/026-8392499-8130832
"Displaying books where Author is Chandor, Anthony, Title is A Dictionary of Computers" BookFinder.com http://www.bookfinder.com/search/?ac=sl&st=sl&qi=OirDDTdbyRailuduqXthXDoEZVg_1594598467_2:1:3
The second reference appears to be to the London periodical "The Accountant"., which you can find by searching major library catalogs, especially in the UK, for the title "accountant".