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. I confined my search to Co. Louth.
1. For Thomas McCann (+variants) B 1833 +/- 4 yrs, I found 5 B rcds: 1829, 1833, 1835, 1836 & 1837. The respective parishes are: Cooley, Louth, Cooley, Haggardstown & Tallanstown. For Jane McCann (+variants) B 1834 +/- 4 yrs, I found 1 B rcd in 1833 in Cooley parish. A view of the detailed rcds SHOULD list the parents' names. This can validate/invalidate the rcd.
2. For a Robert and Sarah marriage, I found 0 Robert M rcds within a wide range. I found 0 Sarah M rcds, ever. The Louth surname exists, but there are 0 B and 0 M rcds for the Sarah forename in Louth, and the rest of Ireland. There are 3 explanations: 1) the event wasn't rcd'd, 2) the rcd didn't survive, 3) your info isn't correct.
3. For a Robert and Jennie marriage, I found 1 M rcd for Robert in 1808. I found 0 M rcds for the surname Hammon (+variants) in Co. Louth, ever. Perhaps they married in a different county. Since I don't find corresponding M rcds for each party, I conclude the event wasn't rcd'd in Louth and the 1808 rcd for Robert is a false positive. You can search in other counties. These have abt 4,000 Hammon M rcds.
4. For the twins, Ann & Bridget, I searched for a common birth yr AND parish 1808-1832. While there were many Ann & Bridget births (some of each in Cooley), I found 0 matching rcds. I conclude the event wasn't rcd'd, or rcd didn't survive.
5. For Mary McCann B 1828 +/- 4 yrs, I found 14 B rcds, 2 in Cooley: 1828 & 1829. For Michael in the same range, I found 3 B rcds, 2 in Cooley parish: 1822 & 1829. A view of the detailed rcds SHOULD list the parents' names. This can validate/invalidate the rcds.
6. The "Sources" show Cooley parish B rcds as continuous from 1811-1900. The evidence for a "Cooley" home would be compelling if the twins also appeared in Cooley. Are you sure you identified the right children as twins?
In any event, this should be a good base to continue your search. Google the Foundation's name to lead you to the database. Post a msg to Genforum to tell me your results.