On the baptism ( Non Conformist ) of their first son John on 7 Oct 1823 the father William is listed as a Husband man.
then
James is baptised on the 10 May 1825 ( Non Conformist) William listed as a Labouer.
then
Son William 1 Feb 1829 baptised George Street Primitive Methodists
then Thomas baptised 2 Jan 1831at Mansfield Woodhouse Nottinghamshire, England
THOMAS then gives us a clue as to what happened to Father William KING on his marriage certificate to Charlotte Buckle 11 Aug 1850 Manchester Cathedral, Lancashire, England the marriage cert states that his Father WILLIAM KING Occupation Oil Cloth maker
Now given that William King ( The father married in 1820 ) I looked for a William King born around 1800c Nottinghamshire and found this.
1851 census
William King 52 born ( 1799) OIL CLOTH MAKER Nottingham, Nottinghamshire
Ann King 32 Born 1819 Birmingham warwickshire
Emma King 9 born 1842 Birmingham Warwickshire
Ann Reynolds 40 born 1911 Worcester, Worcestershire
If you purchase Emma King the Daughter's birth cert That would give her mothers maiden name enabling you to to find William Kings marriage cert to Ann .... This would then give you his Fathers name and occupation with any luck.
Given the age gap between William and his now wife ANN it looks like he remarried the marriage between William King and Ann would give you the father of your William King.
So William King died between 1851 and 1861
1861
Ann King 38 WIDOW Worcester, Worcestershire, England
Ann Reynolds 50 Lodger Worcester, Worcestershire, England
Rosannah Clewell 20 Lodger Bromyard, Worcestershire, England
John David Clewer 8/12 Birmingham, Warwickshire, England
Sorry a long way round to track his background but now you have an approx birth date for William of 1799c born Nottingham and a 2nd marriage to help track his fathers name .
Hope this helps Judi