
"This song has a variety of titles, of which the most common is simply 'The Cuckoo'.
Several singers also use the longer name given here. The songs 'The Unconstant Lover', 'Old Smokey', and 'The Wagoner's Lad' are also thought to derive from 'The Cuckoo'. The parent number has yet to be definitively traced, but it dates at least from the eighteenth century and is probably considerably older.
According to Vance Randolph, a stanza about the cuckoo and its glad tidings appears in a song given in David Herd's Ancient and Modern Scottish Songs (1776). A nursery form of the song can be dated 1796, while another form of the lyric song was published in Glasgow in 1802. Of course, the single verse about the cuckoo and its glad tidings appears in a number of songs, such as that printed in Belden's Missouri collection (p.476). That verse is the one constant in versions of the song.
The cuckoo is a lowly regarded bird that is used symbolically in many ways in western Europe. Because it lays eggs in the nests of other birds, it often stands for adultery. It is also considered a harbinger of summer in Britain, and perhaps both this seasonal and a sexual sense are evident in most versions.
The song is widely known in the American tradition as the Coo Coo Bird.
The coo-coo is the cuckoo, not the modern one which gave its name to mental disturbance, but the old one, the classical symbol of fickleness, false love, of infidelity. The word “cuckold” was derived from the female cockoo’s habit of depositing her eggs in the nest of smaller birds and leaving them there to be hatched by a bird of a totally different species. Another symbolic role of the cuckoo was that it was the herald of spring and was identified with the warmth and promise of that season.
Here are a few versions I collected :

Kelly Harrell - The Cuckoo She's A Fine Bird (original from 1926)
With a cuckoo clock in the background. Clawhammer banjo player from Virginia, born in 1889.

Clarence Ashley - Coo Coo Bird

Hobart Smith - The Coo Coo Bird
Doc & Merle Watson - Cuckoo
Jim Kweskin - The Cuckoo
Mike Seeger - Coo Coo Bird
The New Lost City Ramblers - Coo Coo Bird
Ramblin' Jack Elliott - Cuckoo
Bob Dylan – The cuckoo is a pretty bird (gaslight tapes)
Peter, Paul And Mary - The Cuckoo
Tom Rush - The Cuckoo
John Renbourn - The Cuckoo
Grace Griffith - The Cuckoo
Hem - The Cuckoo
Kristin Hersh - Cuckoo
The Everly Brothers - Cuckoo Bird
The Pentangle - The Cuckoo
Kaleidoscope - The cuckoo
The Be Good Tanyas - The Coo Coo Bird
Townes Van Zandt - Coo Coo
Rick Fielding - Cuckoo
Rory Gallagher - The Cuckoo
Eliza Carthy & Richard Thompson - The Coo Coo Bird
Taj Mahal - The Cuckoo
Telefunk & Willard Grant Conspirarcy
I learned this tune from the Tom Rush Record (a long time ago)
http://lix.in/-23965a
http://lix.in/-251cfb
Oh the cuckcoo
She's a pretty bird
I wish that she were mine
She don't ever drink water
She only drink wine