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