It's OK Sheila ... I'm doing this in support of your quest. Between us we've now got this:
WILLIAM RANDOLPH DAVIDSON was born Abt. 1861 in Ayr, Ayrshire. He married MARY BLACK 02 Jan 1893 in Dunfermline, Fife, daughter of JOHN BLACK and ELIZABETH WISHART. She was born Abt. 1870 in Beath, Fife,Scotland.
Notes for MARY BLACK:
1881 Census Residing at 33 Bruce Street, Dunfermline, Fife - scholar
Children of WILLIAM DAVIDSON and MARY BLACK are:
i. MAGDALENA3 DAVIDSON, b. 26 Jul 1894, Sweerie House, Newburgh, Fife.
ii. MARY DAVIDSON, b. 10 Nov 1896, Sweerie House, Newburgh, Fife.
iii. WILHELMINA DAVIDSON, b. 28 Aug 1898, Sweerie House, Newburgh, Fife.
iv. JOHN WILLIAM DAVIDSON, b. 30 Dec 1899, Sweerie House, Newburgh, Fife.
v. CHARLOTTE DAVIDSON, b. 1901.
vi. THOMAS DAVIDSON, b. 1902.
vii. ALEXANDER WISHART DAVIDSON, b. 15 Jul 1903, Sweerie House, Newburgh, Fife;
d. Abt. 1952, Leith, Edinburgh, Midlothian.
viii. BARBARA DAVIDSON, b. 30 Sep 1907, Sweerie House, Newburgh, Fife.
ix. ROBINA DAVIDSON, b. 30 Sep 1907, Sweerie House, Newburgh, Fife.
Hopefully someone can help from here

Aye mair questions than answers in a world where the past was a different place - that cannae be revisited!!
Chiad Fhear