The above fits these
Northumberland Baptisms on FindMyPast all on same day
All children of Nicolas Coulson and Sarah Wright (who were married 11 Feb 1796, Simonburn, Northumberland)
Bellingham, St Cuthbert, Residence Leehall
Ann b 4 July 1797 bapt 13 Jan 1803 1st daughter
Anthony b May 1799 bapt 13 Jan 1803 1st son
William Coulson b 20 Oct 1801 bapt 13 Jan 1803 2nd son
But if Anthony died 1819, then that leaves William as the eldest......
further baptisms to them on Ancestry
John b 11 Dec 1808, bapt 13 Jan 1809 Bellngham (he is a farmer of 177 acres, employing 6 men in 1851, West Quarter, Hexham)
Nicholas b 18 July 1803 bapt 13 Jan 1809 Bellngham
Thos. b 14 Mar 1806 bapt 13 Jan 1809 Bellingham
can't see Edward yet.
But the one who died 1892 per the MI above left a will
Of Bridgeford, Bellingham, Northumberland, yeoman died 23 January 1892, Probate Newcastle-upon-Tyne 11 March to John Coulson and John Dixon Wright, Farmers. Effects £2138 1s 2d
GRO has him as 81, so born c 1811