Hello ccr1107, the spelling appears to be Harlin in the records I looked at as there are no Harlan names in records I looked at. You have hit a common difficulty, the parish is St Mary's Drogheda, sourth of the Boyne river as you noted. Geographically Drogheda straddles the Boyne and is in County Louth but the parish is geographically in both Louth and Meath as the civil area is divided. St Mary's parish is in the religious diocese of Meath for both RC and Church of Ireland (Protestant).
In the Tithe Applottments there is one Harlin mentioned (1834), a William Harlin in Lagavooren townland. This townland is in both Counties Meath and Louth, then in Griffiths Valuation of 1854 there are plots of land owned or rented by a Rosanna Harlin in Bryanstown (again in Louth and Meath) Wonder if she coud be Williams widow or a daughter.
You can read about townlands elsewhere on this site but basically it is the smallest land description or address that exists but there are in no standard sizes or shapes. You can look here under both counties and see what I am talking about. A word to the wise though both townlands have been extensively developed in the last 20 years and are now mostly but not all urban areas, mainly houses.
https://www.townlands.ie/ you can see the tithes here http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp and Griffiths is here and comes with plot numbers and maps http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
The fact that they were so obviously proud of Meath indicates to me they are from that side of the townland. I reside in this parish. (Louth end) There is a site about Louth and I see a lot of Harlin hits when you search it. If you can see a burial record there I could probably get the inscription, knowing the religion of the people would assist in looking up records as pre 1864 expect for Church of Ireland marriages there are only church records. http://jbhall.clahs.ie/
I see a house holders list for Drogehda in 1837 with a Patrick Harlin in Barrack Lane, which is south of the river also. If you want to spend a nice 10 minutes over a coffee go to You Tube and search Ghosts of Drogheda and you will get a series of old still pictures set to music.
Feel free to revert if you have any follow up queries.
Regards
Pat
