1871 Census just says Wooden, Scotland, for William (living in Northumberland)
Could it be Woodend?
Scotland
Woodend, Aberdeenshire
Woodend, Argyll and Bute
Woodend, Borders
Woodend, Dumfries and Galloway
Woodend, East Ayrshire
Woodend, East Lothian
Woodend, Falkirk
Woodend, Fife
Woodend, Highland
Woodend, Moray
Woodend, North Lanarkshire
Woodend, Perth & Kinross
Woodend, South Lanarkshire
Woodend, Stirling
Woodend, West Lothian
Although a submitted Tree on Familysearch has William christened 5 April 1786
Woodend Aberdeenshire. No Parents named.
Strange to have an exact date with no extra info.
They also have him marrying;
William Black
Spouse's Name Elisabeth Beattie
Event Date 19 Sep 1814
Event Place South Leith,Midlothian,Scotland
Spouse's Father's Name William Beattie
I cant confirm the christening someone else may be able too.
The Marriage is a Parish Record though on F/S.Org
1851 we have in Whittingham;
William Black 65
Elizabeth Black 60
Jane Black 25
John Black 16
William Black 3 Son born Whittingham***
I dont think a 57 year old woman would be giving birth in 1848!
Likely Birth Reg;
BLACK, WILLIAM, Mothers mn MILLS****
GRO Reference: 1847 D Quarter in ROTHBURY Volume 25 Page 375
FreeBMD has a June 1847 Marriage for ROBERT Black to Elizabeth MILLS
Another child;
BLACK, ELIZABETH, MILLS**
GRO Reference: 1849 M Quarter in ROTHBURY Volume 25 Page 436
So likely another Son of William/Elizabeth;
1851 Census
Biddlestone
Robert Black, 27, Head, Mar, Farm Lab, born Northd, Rothbury
Elizabeth Black, 25, Wife
Elizabeth Black, 2, Daug
George Kinghorne, 37, Lodger
1851 we have;
Robert Black 31
Elizabeth Black 34
WILLIAM Black 13**
ELIZABETH 12****
Francis Black 9
Robert Black 7
Benjamin Black 5
Joseph Black 3
John Black 1
All down as born Whittingham, Mayo, Ireland (Mayo, Ireland dittoed from Family above them)
Sorry not much help with your original query.
Trish