1660s, "to utter a low, plaintive, murmuring sound," echoic of doves. Compare, in the same sense, Danish kurre, German girren; also Hindi kuku "the cooing of a dove," Persian huhu "a dove," and see cuckoo.
Meaning "to utter by cooing" is from 1798. Meaning "to converse affectionately, make love in murmuring endearments" is from 1816. Related: Cooing. The noun is recorded from 1729.
What are you doing now,
Oh Thomas Moore?
Sighing or suing now,
Rhyming or wooing now,
Billing or cooing now,
Which, Thomas Moore?
[Lord Byron, from "To Thomas Moore," 1816]
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