do you know James Watson occupation - was he a Tanner - I tend to agree with Redjed 1 .
if he worked with Leather in any of the census returns you might have it could be him ...
Marriage: 21 Dec 1815 St Nicholas, Liverpool, Lancashire, England
James Watson - Tanner, Parish of Liverpool
Ellen Musgrave - Spinster, Parish of Liverpool
Married by Banns by: James Gildart Curate
Register: Marriages 1813 - 1816 from the Bishop's Transcripts, Page 39, Entry 687
Source: LDS Film 1068890
there is no other record for Ellen Musgrave on that site until 1828 and that is a baptism in Rufford - so Ellen Musgrave wasn't born in Liverpool..it looks like their children were baptised in St Peters though - example
Baptism: 26 Oct 1823 St Peter, Liverpool, Lancashire, England
James Watson - [Child] of James Watson & Ellen
Abode: Freeman Street
Occupation: Tanner
Baptised by: J. Pulford Curate
Register: Baptisms 1823 - 1825, Page 102, Entry 816
Source: LDS Film 1656418
I am convinced though that you have the children mixed up - make a note of the address for James - and James occupation - a Tanner
the ones you have listed are for a James and Ellen -- a Shoemaker in Albion Street
Baptism: 18 Mar 1821 St Peter, Liverpool, Lancashire, England
Robert Watson - [Child] of James Watson & Ellen
Abode: Albion St.
Occupation: Shoemaker
Baptised by: T. H. Heathcote Curate
Register: Baptisms 1820 - 1821, Page 243, Entry 1938
Source: LDS Film 1656418
Baptism: 17 Nov 1822 St Peter, Liverpool, Lancashire, England
Sarah Watson - [Child] of James Watson & Ellen
Abode: Albion St
Occupation: Shoe Maker
Baptised by: P. Bulmer Curate
Register: Baptisms 1822 - 1823, Page 148, Entry 2128
Source: LDSNo 1656418
Baptism: 28 Dec 1823 St Peter, Liverpool, Lancashire, England
Ellen Watson - [Child] of James Watson & Ellen
Abode: Albion Street
Occupation: Shoemaker
Baptised by: P. Bulmer Curate
Register: Baptisms 1823 - 1825, Page 157, Entry 1253
Source: LDS Film 1656418 - THIS BAPTISM IS 8 WEEKS AFTER James Watson - so definitely TWO James and Ellen Watson baptising babies at the same time - one a Tanner and one a Shoemaker
Baptism: 24 Oct 1828 St Peter, Liverpool, Lancashire, England
James Watson - [Child] of James Watson & Ellen
Abode: Skelhorne St.
Occupation: Shoemaker
Baptised by: William Goddard Offg. Curate
Register: Baptisms 1828 - 1829, Page 104, Entry 831
Source: LDS Film 93877
moved from Albion street
Baptism: 27 Apr 1829 St Peter, Liverpool, Lancashire, England
William Pettygrew Watson - [Child] of James Watson & Ellen
Abode: Skelhorne Street
Occupation: Shoemaker
Baptised by: J. Pulford, Curate
Register: Baptisms 1828 - 1829, Page 299, Entry 2389
Source: LDS Film 93877