Hi
I found no births to John Monnelly/Munnelly for 1866 in Crossmolina town.
I did find one born in 1865 to John M and Sabina Barrett, but apparently the infant died as in 1874 another John is born to this couple.
In The History of Crossmolina, by Tony Donohoe page 189 is a mention of a Munnelly family from Crossmolina town:
'In the next house where Joe Flagherty lived there was a family of Munnelly's, they came from Ballycorroun and they were tailors, One of them, Willie worked as a tailor in Castlebar'.
In the Ballycarroun chapter, there are, in 1830, a John, James, Frs (Francis?) and Hannah Munnelly leasing land from James Paget. In Griffiths Valuation, there is a John and James Munnelly leasing land in Ballycarroun. There is mention of a marriage in 1841 of a Sally Munnelly marring Pat Haran.
Going back to my spreadsheet, I searched for Munnelly's giving birth during the 1860's in Ballycarroun. I found several families, and also included ones that I couldn't read-thus designated 'CR':
YEAR MONTH CHILD FATHER SURNAME MOTHER SURNAME RESIDENCE
1862 March MARRIAGE John Monnelly Sabina Barrett CR
1871 11-Apr Rose John Monnelly Sabina Barrett Ballycarroon
1874 3-May John John Monnelly Sabina Barrett CR
1859 24-Jun John Francis Monnelly Winifred Lyons Ballycarroon
1876 16-Feb MARRIAGE Patrick Monnelly Bridget Monnelly CR
1841 15-Mar Mary Patrick Monnelly Mary Monnelly CR
1861 July CR James Monnelly Mary Naughton CR
1865 30-Dec Patrick Michael Monnelly Bridget Naughton Ballycarroon
1859 25-Mar CR Maria Michael Monnelly Mary Naughton Ballycarroon
1868 April Edward Michael Monnelly Mary Naughton Ballycarroon
1863 May John Michael Monnelly Mary Naughton Ballycarroon
1876 June Peter Michael Monnelly Mary Naughton Ballycarroon
1877 14-Mar MARRIAGE Patrick Monnelly Margaret Naughton CR
Then I looked up a William Munnelly. I found no male named William under fathers, husband, or sons being born to a William (or any Willie, Will, Bill, ect). Its possible William was born during that the records were missing or I couldn't read the writing.
I have a Mary, Bridgie and Ellen Munnelly attending Enaghbeg Nat'l School in 1912 whose residence is in Ballycarroon- no parents listed.
For McNulty info, again I found no Bridget born within a five year span of 1867. So here are all the John and Mary McNulty couples:
YEAR MONTH CHILD FATHER SURNAME MOTHER SURNAME RESIDENCE
1872 11-Feb MARRIAGE John McNulty Mary Clarke Tawnakeel
1857 26-Aug MARRIAGE John McNulty Mary Corcoran Letterbrick
1879 Feb Eleanor John CR McNulty Mary CR McNally Rcostello
1858 21-Nov Mary John McNulty Mary Doherty Keenagh
1858 16-Feb MARRIAGE John McNulty Mary Doherty Keenagh
1860 March Patrick John McNulty Mary Doherty Keenagh
1868 19-Jul Michael John McNulty Mary Doherty Keenagh
1862 April John John McNulty Mary Doherty Keenagh
1864 May Peter John McNulty Mary Doherty Keenagh
1870 Nov CR Maria John McNulty Mary Doherty Keenagh
1873 6-Apr Catherine John McNulty Mary Doherty Keenagh
Hope I have been of some help!
Diski