The Bodleian Library has a broadside of this with full seven verses

The Irish Emigrant

Full History of the broadside is given and dated to before 1834

Printer: Walker (Durham)
Date:    between 1797 and 1834
   
          Imprint: Walker, Printer, Durham. Printer's Series: (20).
          Illus. Ballads on sheet: 2
          Note: The border and cut are coloured on Johnson Ballads            1567 and Johnson Ballads 1568

   
            
Copies: Harding B 11(239)
          Johnson Ballads 1567
          Johnson Ballads 1568
          Johnson Ballads 1569
          Johnson d.1773(p. 154v)
   
            
Ballads: 1. Ben Block ("Ben Block was a vet'ran of naval renown ..")
             Author: Collins, John
             Subject: Sailors - veterans
            2.The Irish emigrant ("I'm sitting on the stile, Mary ..")
             Author: Dufferin and Clandeboye, Helen Selina Sheridan
             Subject: Emigration - Irish