Some, or most of this, you might already have found but just in case... (this is not in any way a complete family tree). Note: 'Belfast' refers to the registration district as given in GRONI index.
Catherine “Kate” Gaw (c1861 Co.Tyrone-30 Oct.1943 Belfast) m.(14 Jan.1884 Belfast) Thomas William Skinner (d.24 Mar.1904 Belfast). She m.2 (27 Sept.1917 Belfast) Alfred Thomas Billinghurst.
www.census.nationalarchives.ie/pages/1901/Antrim/Clifton/Linwood_Street/962099Administration of the estate of Thomas William Skinner late of 29 Silvio-street Belfast Stager who died 24 March 1904 at The Royal Victoria Hospital Belfast granted at Belfast to Catherine Skinner the Widow. Effects £14 4s.
www.census.nationalarchives.ie/pages/1911/Antrim/Clifton/Hillview_Street/1456411911- 9 children (6 living)
Belfast City Cemetery (F 683): Mr Thomas Skinner, age 47 [death registration says age 46], resided 29 Silvio St., died 24 Mar.1904 Royal Vitcoria Hospital, buried 27 Mar.1904. Josephine Skinner, 8 weeks, 48 Linwood St., died 10 June 1920, buried 12 June 1920. Sarah Uprichard Skinner, 2 months, 51 Linwood St., died 7 Mar.1922, buried 9 Mar.1922. George Herbert Skinner, 5 months, 48 Linwood St., died 6 Sept.1924, buried 8 Sept.1924. Catherine Billinghurst, age 79, 103 Silvio St., died 30 Oct.1943, buried 1 Nov.1943. Moore Skinner, age 78, 64 Alliance Parade, died 13 Aug.1967, buried 15 Aug.1967.
1.
Thomas L. Skinner (reg. Oct./Dec.1884 Dundalk, Co. Louth?-28 Feb.1948 Belfast) m.(4 Feb.1905 Belfast) Ethel/Esther M. Tweedie/Tweedy.
www.census.nationalarchives.ie/pages/1911/Antrim/Shankill/McCandles_Street/152061 1. Annie Skinner (22 Nov.1906 Belfast)
2. Catherine Skinner (24 June 1909 Belfast-11 Aug.1910 Belfast)
2.
Moore Weir Skinner (4 Feb.1889 Belfast-13 Aug.1967) m.(11 Nov.1911 Belfast) Sarah Ann Marks
? Belfast City Cemetery- Public Ground (Z1 239): stillborn son of Moore & Dorothea Skinner, died & buried 16 July 1954. Father possibly the Moore Skinner born 1913 Belfast.
1. Dorothy Skinner (5 Aug.1911 Belfast)
2. Moore Skinner (9 July 1913 Belfast)
3.
Nelson Wilkinson Skinner (27 Dec.1890 Belfast) m.(22 Oct.1911 St. Anne’s Church of Ireland, Shankill, Belfast) Emily Patterson
1. Isabella Skinner (27 Oct.1912 Belfast)
4.
James Skinner (25 Feb.1893 Belfast).
5.
Sydney Skinner (17 Mar.1895 Belfast-2 Jan.1897 Belfast)
6.
Sydney Arthur Skinner (19 July 1897 Belfast-27 Sept.1960) m.(28 Mar.1921 Belfast) Sarah Mary Davison
Belfast City Cemetery- Glenalina Extension (A1 223): Sydney Arthur Skinner, age 61, 14 Selby St., died 27 Sept.1960, buried 29 Sept.1960. Elizabeth R. Caldwell, age 38, 26 Moyne Park Gilnahirk, died 2 Dec.1963, buried 4 Dec.1963. Sarah Mary Skinner, age 85, 8 Eurterpe St., died 17 Aug.1979, buried 20 Aug.1979.
7.
Henry Scanlon “Harry” Skinner (20 Sept.1899 Belfast-5 Apr.1981) m.(26 Dec.1921 Belfast) Margaret Gilliland
Belfast City Cemetery- Glenalina Extension (M 15): Margaret Skinner, age 71, 48 Glenbryn Dr., died 1 Jan.1966, buried 4 Jan.1966. Henry Skinner, age 81, 48 Glenbryn Dr., died 5 Apr.1981, buried 8 Apr.1981.
8.
Essie Tweedy Skinner (27 Feb.1902 Belfast) m.(6 May 1922 Belfast) Francis Johnston
This family tree gives Catherine’s father as Hugh Gaw and there are other mistakes as well but there are lots of names and dates to check.
http://familytreemaker.genealogy.com/users/s/k/i/Moore-Weir-mills-Skinner/WEBSITE-0001/UHP-0039.html