'A pleasant new Ballad of Daphne: To a new tune' appeared on a broadside of the early 17th century, "printed by the assignees of Thomas Symcocke", and later appeared in various chapbooks. It was reprinted in Roxburghe Ballads II, 530: the full text is quoted at http://www.xs4all.nl/~pboot/Daphne/WhenDaphne.htm. That site also has interesting material on the long popularity of the tune in the Netherlands.

Chappell (Popular Music of the Olden Time, I, 338-9) prints the tune with the Roxburghe text in modernised spelling; the text quoted above has been further shortened and altered in places; there's no indication as to where Phyfe got it.

No English broadside example at Bodleian Library Broadside Ballads, it seems; but there is a Dutch song, Liedeken op de vlucht van Daphn, voor Apollo set to the tune. No image is available.

See also notes at Andrew Kuntz's Fiddlers Companion: Hit and Miss and Daphne.

Details (though not the song text) are in Claude M Simpson, The British Broadside Ballad and Its Music, Rutgers University Press, 1966, 163-4.