I searched the Irish Family History Foundation's database. Co. Tyrone and Co. Louth B/M rcds are in it. Ardee parish B rcds exist for the yrs 1763-1815 & 1819-1900. CofI rcds aren't separately listed; only Catholic parishes are. Co. Meath is not online.
Elizabeth Smith's B & M rcds may enter the database when Co. Meath rcds are added. Don't know when.
William Hargrave's B rcds are not in the Cork (north) database. They may be in the mass of undigitized rcds for Cork (south).
Thomas Smith and Sarah Wilson M rcds are not in the Co. Tyrone database. The 1773 date is too early. Donaghmore is listed as a RC parish. There is a separate listing of CofI parishes.
If you had listed the children's names and DOB, I could have searched for those. Will let you pursue this. Google the Foundation's name to lead you to the database.