I searched the Irish Family History Foundation's database for Louth. Rcds B4 1840 are sparse.
For Michael Boyle, B abt 1791, I found 3 B rcds, none in Carlingford. One MAY be for your ancestor. At this early date, only 8 of 20 Louth parishes were keeping B rcds; But, these are the more populous. I rate your chances at abt 40%
For Michael Boyle, M 1818 +/- 4 yrs, I found 1 M rcd in Drogheda parish. M rcds by this date are more complete, but not perfect. Your chances are abt 60%. The CORRECT marriage rcd SHOULD show the maiden name of the spouse.
The children's rcds are the most likely to have survived. For the Children: John B 1826 +/- 2 yrs, 5 B rcds; Lawrence B 1823 +/- 4 yrs, 2 B rcds (1 spelled Lawrence, the other Laurence); Mary B 1821 +/- 4 yrs, 16 rcds.
I suggest you work with the children 1st, starting with the one with the FEWEST rcds and find the parish. The parish for one is often the parish for all. For Lawrence, the parishes are Dundalk and Dunleer. The CORRECT B rcds SHOULD show the names of the parents.
Google the Foundation's name to lead you to the database. Post a msg to Genforum to tell me your search results.