This will give you places to look for Robert.
Hannah Crombie born 29 Sept 1799 christened 10 Nov 1799 the 2nd daughter of Robert Crombie, Pitman, native of Ebbet Saw, Scotland by his wife Elizabeth late Blenkinshop, Native of All Saints
Jane Cromby born 13 June 1803, baptised 3 July 1803 3rd daughter of Robert Cromby, Willington, Pitman, native of Ebitsaw, Fifeshire, by his wife Elizabeth late Blenkinsop native of All Saints Newcastle
John Cromby, born 2 May 1807, baptised 23 Aug 1807 4th son of Robert Cromby, Willington, Labourer, Native of Alnwick by his wife Elizabeth late Blenkinsop native of All Saints
Robert Cromby born 3 Aug 1811 baptised 31 Aug 1811 4th son of Robert Cromby, Willington, native of Scotland, Pitman by his wife Elizabeth late Blenkinsop native of All Saints Newcastle
I imagine your source was the IGI so you know where they were baptised but it looks like they lived and the children were born in Willington.
Your best bet in All Saints for Elizabeth is the later dated one:--christened 9 April 1769, All Saints daughter of James Blenkinsop. The first one had a father of James also so she probably died as an infant. That one was baptised 21 June 1767.
Then there is a marriage of James Blenkinsop to Hannah Burnet 25 May 1766 All Saints.
Both the names James and Hannah are in your children list.
Ebbitsaw is most likely Abbotshall, Fife.
Janis