The following is based on reasonable extrapolation from the limited information available so far for the Donnelly family. I have searched only on the exact surname spelling and limited the search to Shettleston but alternative spellings added little to the mix and additional districts gave too many possibilities. I have not investigated the possibility of forename reuse.
James Donnelly was born about 1836 to Mary Shields and Hugh Donnelly.
Elizabeth Kennedy was born about 1840 in Glasgow to Margaret McKeary and Thomas Kennedy.
1860 On Monday, April 30, James Donnelly and Elizabeth Kennedy were married in St Mary's Church, Calton, Glasgow after Banns according to the Forms of the Roman Catholic Church. The marriage was registered No.75 at Glasgow (Bridgeton) on May 7.
James gave his age as 24 and usual residence Sandyhills. His parents are recorded as Hugh Donnelly and Mary Shields.
Elizabeth gave her age as 22 and usual residence 18 John St. Lane. Her parents are recorded as Thomas Kennedy and Marget McKeary.
The celebrant was E. Noonan and the witnesses Edward McManes, Weaver and Harriet Fean. Elizabeth made "her X mark", the others signed.
Unusually, this registration does not record the marital status of the principals or the occupation of their fathers (or of James).
James and Elizabeth had the following children (that I know of), all born in Shettleston —
Margaret born in 1861, last sighting 1891. Henry born in 1864 in Sandyhills, last sighting 1881. Mary born in 1866 in Sandyhills, last sighting 1891. James born about 1868 in Sandyhills, last sighting 1871. Elizabeth born in 1870 in Sandyhills, last sighting 1891.
1861 April 7 This might be our James, living on his own at 1 McNicol's Land (Upper flat), New Airdrie Road in a house with one windowed room.
Rel. Mar. Age Occupation Birthplace James Donally Head Mar 25 Coal Miner Lanark, Shettleston 1 But where is Elizabeth?
1861 Margaret Donnelly was born at 6h55m p.m. on Sunday, December 8 at Shettleston, Lanark to Elizabeth Donnelly m.s. Kennedy and James Donnelly, Coal Miner who married on April 31, 1860 [sic] in Glasgow. Her birth was registered No.233 at Shettleston on the following day by James Donnelly, Father.
1864 Henry Donnelly was born at 5h30m p.m. on Thursday, September 1 at Sandyhills, Shettleston, Lanark to Elizabeth Donnelly m.s. Kennedy and James Donnelly, Coal Miner who married on April 30, 1859 in Glasgow. His birth was registered No.174 at Shettleston on September 3 by James Donnelly, Father.
1866 Mary Donnelly was born at 4h0m p.m. on Wednesday, June 6 at Sandyhills, Shettleston, Lanark to Elizabeth Donnelly m.s. Kennedy and James Donnelly, Coal Miner who married on April 31 [sic], 1859 in Glasgow. Her birth was registered No.133 at Shettleston on June 11 by James Donnelly, Father.
1868 James was born.
1870 Elizabeth Donnelly was born at 7h0m p.m. on Sunday, December 18 at Sandyhills, Shettleston, Lanark to Elizabeth Donnelly m.s. Kennedy and James Donnelly, Coal Miner who married on April 30, 1860 [sic] at St Mary's, Glasgow. Her birth was registered No.269 at Shettleston on December 22 by James Donnelly, Father.
1871 April 2 The family were living in Sandyhills Square in a house with one windowed room.
Rel. Mar. Age Occupation Birthplace James Donnely Head Mar 36 Miner (Coal) Ireland 1 | 1 Elizabeth [Kennedy] Wife do. 32 Lanarkshire, Shettleston Margaret do. Daur 10 do., do. Henry do. Son 6 Scholar do., do. Mary do. Daur 4 do., do. James do. Son 2 do., do. Elizabeth Donnely Daur 3mos Lanarkshire, Shettleston
1871 James Donnelly, Pauper (formerly a Coal Miner) married to Elizabeth Kennedy died at 2h10m a.m. on Saturday, August 5 at 10 Square, Sandyhills, Shettleston, Lanark, age 36 years, of Bronchitis Chronic after 3 years, as certified by William Young, Surgeon. His parents are recorded as Hugh Donnelly, Coal Miner and Mary Donnelly m.s. Shields, both deceased. His death was registered No.104 at Shettleston on August 7 by Andrew Donnelly, "his X mark", Brother, residing at Eastmuir Street, Present.
Thomas Dunigan was born on May 22, 1836 in Shettleston, Lanarkshire to Mary Smith (c1807 - 1897) and Henry Dunigan (c1801 - 1870). [See Section DG-5-2 for family background.]
Elizabeth Kennedy was born about 1840 in Glasgow to Margaret McKeary and Thomas Kennedy. [See above for previous marriage.]
1876 On Tuesday, June 13 Thomas Dunigan and Elizabeth Donnelly were married at Eastmuir, Shettleston [St. Paul's] after Banns according to the Forms of the Roman Catholic Church. The marriage was registered No.29 at Shettleston on June 15.
Thomas was a Bachelor, gave his age as 38 [he was 40], occupation Mineral Borer and usual residence Shettleston, Lanark. His parents are recorded as Henry Dunigan, Cotton Weaver, deceased and Mary Dunigan m.s. Smith.
Elizabeth was a Widow, gave her age as 36 and usual residence Shettleston, Lanark. Her parents are recorded as Thomas Kennedy, Police Officer and Margaret Kennedy m.s. McCarey, both deceased.
The celebrant was George McBrearty and the witnesses were Henry Dunigan and Ann Donnelly.
Elizabeth and Ann made their marks, Thomas and Henry signed.
The marriage is recorded in the Parish of St Paul's, Eastmuir where Ann Donnelly is Mrs Ann Donnelly.
Thomas and Elizabeth had the following children (that I know of) —
Thomas born in 1878 in Green Street, Shettleston, last sighting 1891.
1878 Thomas Dunigan was born at ?0h30m p.m. on Monday, December 2 at Green Street, Shettleston, Lanark to Elizabeth Dunigan, formerly Donnelly m.s. Kennedy and Thomas Dunigan, Mineral Borer who married on Jun 13, 1876 in Shettleston Parish. His birth was registered No.292 at Shettleston on December 9 by Thomas Dunigan, Father.
He was baptised in the parish of St Paul's, Shettleston on December 13 by Fr. George McBrearty with sponsors Widow Mary Donegan and James Donnelly.
1881 April 3 At 25 Patterson's Land, Shettleston in a house with one windowed room, there dwelt
Rel. Mar. Age Occupation Birthplace Thomas Dunnigan Head M 44 Mineral Borer Lanarkshire, Shettleston Elizabeth do. Wife M 40 do., Glasgow Thomas do. Son U 2 do., Shettleston Margaret Donely Step Daur U 19 Bleachfield Worker do., do. Mary do. Step Daur U 14 Mill Girl Silk do., do. Henry do. Step Son U 16 Roper do., do. Elizabeth do. Step Daur U 10 Scholar do., do.
1884 On Thursday, February 14, John Connor and Mary Donnelly were married at St. Paul's R.C. Church, Shettleston after Publication according to the Forms of the Roman Catholic Church. The marriage was registered No.14 at Shettleston on the same day.
John was a Bachelor, gave his age as 23, occupation Coal Miner and usual residence Lightburn, Shettleston. His parents are recorded as James Coner [sic], Labourer and Helen Coner m.s. Fitzcharles.
Mary was a Spinster, gave her age as 19 [she was 4 months short of her 18th birthday], occupation Bleacher and usual residence Carntyne Street, Shettleston. Her parents are recorded as James Donnoly [sic], Coal Miner (deceased) and Elizabeth Dunnigan [sic], previously Donnoly m.s. Kennedy.
The celebrant was Geo. McBrearty, Cath. Clergyman and the witnesses were Henry Donnelly and Margaret Donnelly [probably Mary's brother and sister].
Mary and Margaret made their marks, the others signed.
1891 April 5 The family were living at 3 Albert Place, Shettleston in a house with two windowed rooms.
Rel. Mar. Age Occupation Birthplace Thomas Dunigan Head Mar 65 Mineral Borer Lanarkshire, Shettleston 2 Elizabeth do. Wife do. 50 (late) Mill Worker do., Glasgow Margaret D. do. Daur Unm 28 do. do., Shettleston Elizabeth D. do. do. do. 20 do. do., do. Thomas do. Son 13 Scholar do., do. Elizabeth Connor Gr.Daur 7 do. do., do. This looks like the rest of the Connor family in High Carntyne, in a house with four windowed rooms.
Rel. Mar. Age Occupation Birthplace John Connor Head Mar 32 Coal Miner Lanarkshire, Shettleston 4 Mary [Donnelly] Wife do. 24 do., do Helen do. Daur Unm 5 do., do. Margaret do. do. do. 2 do., do. Henry do. Son do. 11mo do., do. And not far from them, also in High Carntyne in a house with one windowed room, is another family who might be connected.
Rel. Mar. Age Occupation Birthplace William Connor Head Mar 25 Ag. Lab. Lanarkshire, Shettleston 1 Rachel do. Wife do. 24 do., do Mary do. Daur Unm 5mo do., do.