Morgiana in Ireland (sometimes Morgiani) turns up in a whole cluster of MS tunebooks, tutors and so on from around the first decade of the 19th century onwards, along with Morgiana / Morgeana / Morgeanne, which appears to be a little earlier, Morgiana in Spain, and Morgiana in England. Probably the other tunes are "sequels", so to speak, to Morgiana, which was evidently popular. In such cases (and without being in a position to check at the moment) the usual explanation is that the tune is from a popular stage show of the day; quite possibly a pantomime, which were very elaborate affairs in those days.

Morgiana in Ireland seems to have been the biggest success of the group. J. Blewitt (who wrote -presumably- the popular slip-jig Barney Brallaghan, originally as the music for a comic song) published an arrangement of it as a rondo for piano, and it was used as the tune for several songs, for example

Lavender Girl (Lester Levy Collection, n.d)

and the thoroughly odd  Rimes's Alley  (Bodleian Library).