This phrase was coined in 1983 by sociologist Arlie Russell Hochschild in her book
The Managed Heart: Commercialization of Human Feeling. The earliest media citation I could find for this phrase occurred in a capsule review of this book (see below). Here's the first citation I could find that doesn't reference this book or Ms. Hochschild:

In the old days, says Dr Georgiades, running an airline meant making sure the same number of planes came down that went up. Now it's all about 'emotional labour.'
Bryan Appleyard, "Spectrum: An airline forever grounded?," The Times, July 24 1986
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