I think somewhere you mentioned a Livingston connection to John Harrison, father of James. I am also looking at Harrisons in that area and have come across something without enough details to know what is going on.
Pierce Livingston, Jr of Ballydougan died in 1860 and mentions John Harrison Jr of Lisnaminty owes him money and also appoints John Harrison as executor. Pierce says daughter Ann Jane married Joseph Davidson and is perhaps Joseph Davison married to Eliza (Ann or Jane) Livingston in records. The other person who borrowed money from him is David England who may be the one with a Davison wife. I think he loaned money to relatives.
John Jr 's known children were James b abt 1858 and Henry b abt 1854 baptized at Knocknamuckley where John d. 1885 @71 and wife Sarah d 1898 @81 are buried. There is a fair chance this is your James. Sarah appears to have moved off the farm after John's death as the land does not appear in her name. Possibly a death certificate could tell you whom she was living with.
The PRONI land records show John Jr name crossed off his land leaving John Sr. However when a father died and a Jr had a son with the same name, Jr became Sr. So I would carefully look at the records and civil death records. John Sr, was b 1787, married Margaret b 1796 and had Elizabeth b 1823, John Jr. and possibly Valentine b. abt 1823.
The other executor is George Somerville from my line and he, Pierce, and John,Jr Harrison appear to be farmers with probably sizable amounts of land and money. You might look to see if the Davisons were related or if Scottish Harrisons had money at first. Livingstons at Seagoe were posted on-line, but i don't see a Harrison connection.
The Henry Harrison who appears in Lisnamintry in the census is the illegitimate son of Margaret Malcomson whom she had by a Henry Harrison of Ballygargin, she claimed. Her brother Joseph left him the home. No idea which Henry is involved.