See also this site:

"We'll Sing to Abe Our Song!": Sheet Music about Lincoln, Emancipation, and the Civil War from the Alfred Whital Stern Collection of Lincolniana (Library of Congress)

The most famous--if not most popular--composition of "We Are Coming", I think, is by Stephen Foster.

We Are Coming Father Abraam, 300,000 More (note the spelling as "Abraam"; 1862; Music Composed by Stephen C. Foster). Original sheet music is HERE too. MIDI & lyrics are HERE and at other Foster sites.

As for the author of the poem:

"In 1862, no less than sixteen different composers, among them Stephen Foster, wrote musical settings for John Sloan Gibbon's poem 'We Are Coming, Father Abraham, Three Hundred Thousand More.' Gibbons, a financial expert by profession and a Quaker by religion, had been moved to write the poem by Lincoln's call in July 1862 for three hundred thousand more troops after McClellan's disastrous failure in the Peninsular Campaign. The poem was anonymously published in the New Yok Evening Post (July 16, 1862), and because the author was not identified, it was generally assumed that it had been written by the editor of the Evening Post, William Cullen Bryant, himself a distinguished poet; a number of the composers credited Bryant with the text." (Vera Brodsky Lawrence, Music for Patriots, Politicians, and Presidents, Macmillan, 1975, p. 364)

Another title is used by this edition:

Three Hundred Thousand More! (1862; Music by G.R. Poulton)

~Masato