Unfortunately not much is known of Mary's family. Given that Mary was married in the parish of Solohead (formerly spelled Solloghod) at a time when marriages typically took place in the bride's parish, it's possible the Hanleys came from that parish. Another possibility is that, given that the neighbouring parish of Soloheadbeg (formerly Solloghodbeg) used the Solohead church, and given that Mary's husband probably came from Soloheadbeg, the Hanley family may well have come from Soloheadbeg.
According to records from Tipperary Family History Research, the marriage of Mary and Edmond was witnessed by Thomas Carey and William Carew.
Besides the surnmames Hanley and Carew, names that occur more than once amongst the godparents of the children of Mary and Edmond are Godfrey and Ryan, so it's possible the Hanleys and the Carews were related somehow to these families.
There's a possibility that our Hanleys might be connected to the Hanley family of Margaret Lloyd from New Zealand. Margaret's great-grandmother, Ellen Hanley, was born in Solohead in 1818 to Michael Hanley and Ellen Lonergan (her baptismal sponsors were William Meighan and Mary Ryan). Sometime afterwards, possibly between 1830 and 1843, Ellen's family was evicted from their farm in Solohead and they subsequently moved to Cooga in the parish of Doon, Co. Limerick. Family lore has it that the Hanley farm was on Lord Stanley's estate and could be seen from the the big house, as a result of which the residents wanted to be rid of the tenants, hence the eviction. It's possible they were offered alternative land in Cooga by Lord Stanley because in Griffith's Valuation (1850s), Lord Stanley is shown to be their landlord in Cooga. Descendants of this Hanley family still live in Cooga.
I've been unable to make a connection between Margaret's Hanley family and mine but just in case they are related, here are some more details about her great-grandmother's family:
Ellen had a sister named Julia who was born in 1815 (baptismal sponsor was William Lonergan). According to Julia's baptismal certificate, the family lived in Kilmurry (there are Kilmurrys near Carrick-on-Suir and Clonmel in Co. Tipperary but it seems more likely the Hanleys lived in Kilmurry, Co. Limerick, which is closer to Solohead). Ellen also had two brothers, Michael who was born in 1821 (baptismal sponsors were John Lonergan and Honora Lonergan) and John, born 1824 (sponsors were William Cranitch and Margaret Godfrey). It seems that Ellen (mother of Julia, Ellen, Michael and John) died shortly after John's birth because it appears her husband Michael married Johanna O'Doherty in 1826. They had a son, Cornelius, in 1827 (sponsors were were Edmond Hanley and Catherine Leamy), who must have died in infancy because a second son named Cornelius was born in 1828 (sponsors were John Doherty and Johanna Doherty). Cornelius married Hanora Carew in 1856 in Galbally and their children, born in Doon, were Bridget, born 1859 (baptismal sponsors were Julia Hanley and John Hickey); Eliza, born 1859 (sponsors Bridget Madden and Michael Tobin); Richard, born 1865 (William Coffey and Catherine Coffey); Mary, born 1867( Daniel Tuohy and Margaret Hickey); Patrick, born 1869 (John Hanley and Julia Hanley); Julia, born 1872 (Richard Lloyd, Catherine Hickey); and Hanora, born 1878 (James Carew and Bridget Hickey).
Ellen married Patrick Tobin in Doon in 1843 and following his death she married John Lloyd in Doon in 1853. Witnesses to Ellen's marriage to John were Conor (Cornelius) Hanley and Bridget Hanley, and among the sponsors at their children's baptisms were T. (Thomas?), Con, Julia, Patrick, Kitty and Bridget Hanley. Richard Lloyd, a son of John and Ellen and grandfather of Margaret, emigrated to Christchurch, New Zealand around 1877.
I have also been in contact with Michael H. Ryan who is a descendant of Thomas Ryan (believed to have been from Soloheadbeg) and Julia Hanley who married in Solohead/Oola on 21 January 1854. Could Julia have been related to our Hanleys? In case there is a connection, here are some details on the children of Thomas and Julia:
Thomas, born 1855, probably in Soloheadbeg
Thady (aka Timothy), baptised 30 July 1856 in Tipperary (ancestor of Michael H. Ryan)
Bridget, baptised 8 December 1857 (although Michael halso has a baptismal date of 18 February 1857 for possibly the same person - could the first Bridget have died?)
Richard (although no documentation has been located for him)
Note: The Hanley surname is numerous throughout Ireland, especially in north Munster and in Connacht. The Hanleys were originally a sept of Co. Roscommon. The Irish form of the name is "Ó h-Áinle" from the Irish word "áinle" meaning "beauty".