‘shearg’ last post was Nov 2017, i hope he is still interested.
I started for Morgan anywhere in ireland/ Could she be the daughter of any of these 1819 men in Belfast street directory see
Morgan, John, grocer, 87 North Street
Morgan, Thomas, grocer, 8 Old Barrack Street
Morgan, David, brick layer, 6 Meeting House Lane
her religion would help eg Church of Ireland births exist for St Anne, Shankill (now Belfast Cathedral) 1745-1871 note from
RCB Dublin says A published version of the earliest register 1745-1761 with index is available for purchase from the RCB website.
Some coverage at RootsIreland.ie PRONI BELFAST has an online guide to Church records the entry reads
C.I. St Anne’s, Shankill (Connor diocese)
Baptisms, 1745-1901; special baptisms, 1817-66; marriages, 1745-1900; burials, 1745-71, 1784-1809 and 1824-65,1878 and 1883; index to baptisms, 1745- 1866 and 1872-84, to marriages, 1745-1823, and to burials, 1745-1812.
Baptisms, 1872-1901; indexes to baptisms, 1872-84; marriages, 1845-1900.
Burials, 1884-; vestry minutes, 1808-1934; registers of vestrymen, 1870-.
[There is a printed volume containing transcripts of marriage entries, 1745-99] the material has microfilms, presumably the cathedral has a copy themselves
presbyterian non subscibers have N.S.P. Rosemary Street (1st)
Baptisms, 1757-1977; marriages, 1790-1930
P. Rosemary Street
[Baptisms from 1868-1941 destroyed during the 2nd World War]
Baptisms, c.1723-1867, with an index; marriages, c.1741-1846, with an index;etcetc
R.C. St Patrick’s (Donegall Street) (Down and Connor diocese)
Baptisms, 1798-1811, 1814-67 and 1875-80; marriages, 1798-1812 and 1814-67.
So there is a possibility you might pick up her birth and more info on parent/parents from church records but move out from the cities of Ireland and there few church existing records before 1820, much lost in irish historysee 1916, 1921- 2 etc.
Morgan in Ireland is represented in most counties see Griffiths quick index 1848-1864 https://www.failteromhat.com/post1845.phpSo the odds are stacked against your search even with jstaffor terrific wedding help
there is always the luck of the irish so could something further turn up
STOP THE PRESS Suppose Susannah age is 5 years out, and the Belfast family arrived in New York on their way to Toronto. I have just stumbled on a James Morgan and family Belfast arriving as passengers by the ship Africa, John E. Scott, Master, from Belfast, arrived June 9th.New York see
http://www.dippam.ac.uk/ied/records/47745 Vol. 1, No. 27, Sat. Jun. 15, 1811.
Extracts taken from an article published in:-
THE IRISH GENEALOGIST, Vol. 6, No.4, 1983, pp. 370-377; No.5,
1984, 495-507. Notices taken from the Shamrock Newspaper of
New York 1810-1812: I Passenger Lists II Marriages in Ireland III Deaths in Ireland IV Miscellaneous Extracted by John Devereaux Kernan.
Extracts from 'The Shamrock or Hibernian Chronicle', a
weekly newspaper published in New York 1810-1817. The Volume
from which the information is taken, is held in the Sterling
Library of Yale University, New Haven, Connecticut. However,
it is not complete, as 54 issues of the run are missing,
mainly in 1812. I PASSENGER LISTS
so lots of good luck that’s as far as I can help