In 1855 Galway there were 83 occupiers of land with the name Rabbitt. 5 of these are James Rabbitt's. 104 Dillon's in Galway, depending on the dates this maybe their parents. See www.askaboutireland.ie
None are listed with Castleblakenay but Castleblakenay is also a Union where all parish's, townlands, villages within a 12 mi. radius are located. An administrative area for the Poor Law Union and later Civil Registration Districts.
Civil registration Ireland 1864-1875
No children listed for James Rabbit and Honora Dillon?
There are James Rabbit's born between 1861-1867.
Jacobus Rabbit born 14 May, 1861 Baptism 25 May 1861, Killian and Kilronana, Galway
Fa: Patritio Rabbit Mo: Brigida Ward FHL FIlm #989748
James Rabbit born 17 Nov 1866 #604 Tuam, No 2 Galway
Fa: Timoty (Timothy?) Rabbit Mo:Honor Hopkins #101138
James Rabbit born 23 Dec 1867 #__Abbey, Galway
Fa: James Rabbit Mo: Margaret Ward #101163
Honoria Dillon born 12 Dec, 1870 baptism 17 Dec 1870
Killian and Kilronan, Galways
Fa: Martino Dillon Mo: Catherina Connelly #989748
Honor Dillon born 12 Aug 1871 #406 Killeroran, Galway
Fa: Thomas Dillon Mo: Honor Smyth #255829
Honor Dillon born 22 Feb 1872, Killeroran, Galway
Fa: Martin Dillon Fa: Catherine Connelly #255854
Honor Dillon born 21 Jan 1874 Clonbrock, Galway
Fa: William Dillon Mo: Mary Lyons #255896
Honora Dillon born 15 Jan 1874 Glennamaddy, Galway
Fa: James Dillon Mo: Catherine Donlon #255896
Perhaps some of these might fit.
If before 1864 you need to try an Irish History Foundation for Parish records. Galway is divided genealogically into
East and West and both are members, like most Irish genealogy records are not free although the Foundation is
a not for profit.
After 1864 civil registrations like above are available on the Latter Day Saints website www.familysearch.org
and records are available there to about 1950's.
If were still in Ireland by 1901/1911www.census.nationalarchives.ie
There are several Rabbit/Rabbitts in the commercial directories for Galway.
Castle-Blakeney was described in 1846 as a small post-town
and Parish. The parish was also known as Gallagh or Killosolan. 31 M. from Galway and 16 1/2 from Athenry on the
road to Tuam.
Roderick Rabbitt, was Post Master in 1846.
5 Rabbitt's in the current Galway phone book 2 in Athhenry
area. A few stamps and letters might prove successful.