The Twibills are very hard to trace. Here's what I found. Maybe some of it is useful to you.
The National Archives WO97: Royal Hospital ChelseaL Soldiers Service Documents (I have these if you want copies)
Subseries within WO07: 1760-1854: discharge papers arranged by regiment, but each described at item level (WO97/1-1271)
WO 97/1267 Royal Artillery: TRO-VOS, Covering Dates 1807-1824
George Twible, born Castleblany, Monaghan, Served in Royal Artillery, Discharged age 33
WO97/549 38th Foot: Smi – You
William Twibill, Born Castleblaney, Monaghan, Served in 38th Foot Regiment, Discharged aged 40
Muckno Parish Records
Castleblayney Co. Monaghan
1.1817, 27 Sept, George Twibill son of George Twible Knockavolis
2.1820, 2 April, Jane daughter of George & Betty Twible Knocavolis
3.1824, 11 June, Robert, son of George & Eliza Twible Knockavolis
4.1828, 31 August, William, son of George and Jane Twyble, Banagher
5.1830, 4 July, Jane daughter of George and Mary Twyble, Drumnakile
6.1831, 11 June, Elizabeth, daughter of Joseph and Elizabeth Twybill, Castleblayney
7.1833, 17 Feb, Alley, daughter of George & Jane Twibill Drumnakile
8. 1835, 25 July, Jane, daughter of George & Jane Twibill Drumnakile
9.1836, 20 July, Hannah, daughter of George & Jane Twybill Farmer Drumnkile
10.1840, 3 Sept, George son of George & Jane Twybill Farmer Drumnkile
11.1840, 3 Sept, Eliza, daughter of George & Jane Twybill Farmer Drumnkile
12.1844, 12 May, (DOB) Margaret, daughter George & Jane Twible Farmer Drumnkile
13.1849,26 Nov. William , son of William & Mary Twible Castleblayney, Master and Matron of Union Workhouse
Marriage
27 July 1830, Joseph Twybill & Eliza Twybill, Castleblayney, note (to America)
MARRIED.
In the Church of Castleblayney, on the 27th ult.,
Captain J. Twible, of the American Ship POTOMAC, of New
York, to Eliza, youngest daughter of Munday Twible, Esq.,
late of Castleblayney, deceased.
Marriage of Captain J. Twible to Eliza Twible
SOURCE
The Belfast Newsletter, Friday, August 6, 1830
ARCHIVE
The Central Library, Belfast
14 June 1850, William Barker of Newtownhamilton to Eliza Twibill, father Joseph Twibill, sea Captain from Hulltown? (see above)
Burials
1811, 27 Dec Monday Twibill, Castleblayney Aged 80
1832, 8 Oct, Martha Twybill, Castleblayney Aged 64
1855, 2 June William Twibill, Castleblayney Workhouse Aged 59
Twibill gravestone in Castleblayney garveyard Badly weathered
William Twibill October 1791 aged 94?
Mary Twibill June 24 1793 aged 35? 85?
Munday Twibill December 24 (1811)
other names badly weathered
William Twibill
Matthew Twibill b. 19 April 1793
another date at the bottom 16 January 1847
1st Castleblayney Presbyterian Records
Baptisms
Children of John Bailey and Anna Maria Twibill 9of Drumillard then Castleblayney 1842)
1836 18 March DOB, Thomas
1842, 15 April DOB, Maria
1846, 8 May, John (to Anna Maria Twible)
1848, 14 July, Margaret
1852, 10 August, Anna
Marriage
26 July 1858, David Lockart Clerk of Dundalk to Mary Twibill, widow of Castleblayney, father Antony Dugan, Merchant.
Broomfield Presbyterian Church
Marriage
23 May 1850 Hans Hamilton farmer Gorteens father Hans Hamilton to Eliza Twible Knockagolis father George Twible,
Witness Moses Hamilton & John Twible
8 January 1856 John Twibill, farmer Knockagolis father George Twibill married Mary Hillis (Minor) Cabra Bally bay, father James Hillis, witness Matthew Twible.
28 July 1866 John Ralston Widower, Hotel proprieter & farmer, Castleblayney married Eliza Hamilton Castleblayney, father Hans Hamilton, witness Sally Anne Hamilton
28 April 1871 Eliza Hamilton father Andrew Hamilton & George Hamilton Gilmer merchant
22 January 1903 Hans Hamilton, Gourteens father Hans Hamilton married Anna E. Kinghan Ardkirk father James Kinghan witness Thomas Hamilton
Broomfield Baptism
DOB
28 July 1843 Robert, son of Mundy Matthew Twibble & Isabella Hill Knockagolis
13 April 1851, Jane, daughter of Hans hamilton & Eliza Twible Gorteens
19 April 1850, Robert, son of John Twibble & ** Greer, Knockagolis
1 June 1857, Robert, son of John Twibble & Mary Hillis, Knockagolis
3 April 1860, Hannah, daughter of John Twibble & Mary Hillis, Knockagolis
17 November 1862, Jane, daughter of John Twibble & Mary Hillis, Knockagolis
11 May 1893 Andrew, son of Andrew hamilton & Isobel Mitchell, Wellington New Zealand
Broomfield deaths recorded in the Baptism book.
John Twible Knockagolis 23 August 1864 age 48 of consumption
George Twible Knockagolis 24 December 1868 aged 85 years of old age
Elizabeth Twible Knockagolis 25 April 1875 age 86 years of old age
Eliza Hamilton Drumdreena 30 August 1884, age 70 years of dropsy
Sarah Twible Knockagolis 29 June 1891, age 37
Isabella Twible 8 march 1906, no age given
Broomfield Communion roll
Matthew Twible an elder, received from Corlea Presbyterian Church November 1873
1846 George Twible & John Twible both members
George & Eliza Twible on the roll 1858
1860 George Elizabeth & John
of interest
Thomas Jordan removed on his emmigration to New Zealand 2 August 1875
George Twible emmigrated to Canada January 1883
readmitted on return from Canada 1890
emmigrated 1895 to usa
Matthew Twible the church Elder, moved to 1st Castleblayney.