Quite possibly:
1851 Census Ballamoor Patrick HO107/2523 p 15
William Cringal head m 44 Farm lab. b St. Ann
Ann Wife m 40 b Braddan
George s 10 b Braddan
Elizabeth dau age unreadable 2 or 8? b Patrick
John son 5 b Patrick
Eliza dau 1 b Patrick
I think that this is Ann Shimmin.

1861 census Ballamoor Patrick RG9/4427 p 15
William Cringle (transcribed by Ancestry. com as Crugle) head m 50 Farm lab. b Patrick
Ann Wife m 42 b Patrick
Eliza dau 11 b Patrick
James s 5 b Patrick
Mary A dau 3 b Patrick
William s 1 b Patrick

From the 1851 census George 20 is a servant in Malew with William and Elizabeth Fargher but I can find no match for Elizabeth or John.

It would be worth checking Brian's 1841 census index, which I do not have available here.
The only William Cringle marriage in the IGI that fits is with Ann Shimmin.
The IGI shows them having three children: George chr. July 1838 in Braddan. Elizabeth Ann chr. April 1843 in Patrick and John chr. June 1845 in Patrick.
Ann's maiden name at the christenings the youger children is not given. I wondered if it is the same Ann.
The only suitable Ann Shimmin christening in Patrick is on August 2 1812 (the daughter of John Shimmin and Eleanor Gell). The corresponding age in the 1851 census would be 38 or 39.
In 1881 Ann Cringle widow 66 b Patrick is in German with two grandchildren Eliza Cringle 11 b. Patrick (probably the Eliza Kelly, Elizabeth's daughter from the 1871 census) and Elizabeth Quilliam 1 b Braddan.
She is probaly the one on Brian's birth index born on September 10 1879 to James Quilliam and Elizabeth (transcribed as Craigle).
Finally Brian has a burial record for Anne Cringle age 78 on January 22 1889 in Patrick.
So if it is the same person you have possible DOBs of 1812 (IGI), 1811 (1851 census), 1819 (1861census), 1821 (1871 census), 1815 (1881 census) and 1811 (burial index).