I searched the Irish Family History Foundation's database. It contains 11,500,000 surviving rcds for abt 60% of Irish counties. Rcds B4 1840 are sparse.
For a marriage of Lawrence & Margaret M 1823 +/- 2 yrs, I found 4 rcds for Margaret, 1821, 1823, 1824, 1825 and 1 rcd for Lawrence in 1821. Both Ms are in Haggardstown. This looks like an exact match. Will let you view the detailed rcd to see if the marriage was to each other. If so, the rcd SHOULD show their parents' names.
You can also search for offspring (assuming they were all born in the same parish). I did this and found 215 Kellys born in Louth in a 9 yr span.
Google the Foundation's name to lead you to this database.