I think you're looking for Thomas Joseph Caine ch 14 Oct 1855 Patrick son of John Caine and Eliza Creer who md 21 Aug 1836 in Braddan.
John died of smallpox 7 Jul 1863 Patrick and was buried in Patrick 9 Jul 1863.
Children all christened in Patrick
1. Mary 19 Feb 1837
2. Catharine 16 Dec 1838
3. John 9 Feb 1840 buried 20 Dec 1840 Pat age 12 months page 8 BReg
4. Daniel 29 Jan 1843 md 25 Jan 1872 Kirk German copy of certificate #31
Drusilla Ann Garrett daughter of Thomas Garrett one of those present
Richard Garrett
5. Ann 22 Sep 1844
6. Thomas 24 May 1846 buried 26 Jun 1854 age 8 page 7 Pat Bur Reg
7. Eliza Caine 30 Apr 1848 (msg says she married Ben Gilbert)
8. Wm Caine 14 Apr 1850
9. Joseph 8 Oct 1852 buried 8 Oct 1854 Patrick died from small pox per pg 7 Pat Bur Reg
10.Louisa Jane Caine 9 Apr 1854 Patrick married John Callister bachelor
Mariner on 8 Feb 1872 Kirk German Certificate #32 his father was William
Callister farmer Bracknbroom(Breck y Broom).
11. Thomas Joseph Caine 14 Oct 1855 Patrick.

1851 Census
Ballacosnahan Patrick
John 38 Lead Miner b Patrick, Eliza 39 b Marown, Mary 13 scholar, Cath 11 scholar, John 8 scholar, Daniel 7 scholar, Ann 6 scholar at home, Thomas 5 scholar, Elizabeth 2, William 10 months