Jack of the Green; Oswald's Caledonian Pocket Companion, bk, 2, p.2, c 1745
Jack of the Green; C & S Thompson's 120 hornpipes, c 1775, p. 7:
Jack on the Green; Walsh's Caledonian Country Dances, I, 33, c 1734: Jack on the Green; Bodleian Young MS, 1734: Jack on the Green; Rutherford's 1st coll'n of 200 Country dances, c 1756, 32: Jack on the Green; Thompsons' 1st collecion of 200 country dances, c 1758, 92:
Jack on the Green; O'Neill's Music of Ireland #1149.
Jack o' the Green; Folger Shakespeare Lib. MS, c 1760:
Jack on the Green; Rileys' Flute Melodies, I, 83, 1814:
Jack on ye Green [I]; BL MS Add'l 23971 39b (c 1770):
Jack on ye Green [II]; BL MS Add'l2 3971 100b (c 1770):
Jack in the Green Irish; O'Farrell's Pocket Companion, II 70 (c 1810), Jack in the Green; Haverty's 'One Hundred Irish Airs, 2nd series, #124, (1859): Jack in the Green; Levy's Dance Music of Ireland, I, 1 (1858).

I don't have copies of all of these.