Notes:

NOT PROVEN !
The search for father of Charles Henry Douglas 1853 (app):

Charles Henry DOUGLAS
1881 census - aged 27 born in Doncaster
Marriage certificate to Annie Maria PEACE in 1874 aged 21 living in Rotherham.

I have searched the national birth indexes +/- 5yrs with no luck

Doncaster RO have searched 5yrs and surrounding districts 1852 - 1854, again with no result. (email dtd 18/8/2008)

However,

I wonder if this is him on the 1861 census for Brightside Bierlow ?

Charles BUTCHER 29 shingler b Gresbro?
Harriet BUTCHER 36 b Doncaster
Eliza BUTCHER 5 b Derbyshire
William BUTCHER 5 Mo b Gresbro
Charles DOUGLAS 7 stepson b York
(RG9; Piece: 3499; Folio: 53; Page: 41)

Search for earlier census
1851 census for Doncaster:
Harriet DOUGLAS widow 29 b Doncaster shop keeper
plus some lodgers and a visitor
(HO107; Piece: 2347; Folio: 116; Page: 22)

Search for Marriage
Marriages December 1854
BUTCHER Charles Sheffield 9c 355
DOUGLAS Harriet Sheffield 9c 355

Marriage Certificate ordered and confirms Harriet was a widow and her father was Charles SAYLES.

Search for earlier marriage
Marriage Sep 1842
DOUGLAS John Doncaster 22 41
SAYLES Harriet Doncaster 22 41

Search for death
Death Dec 1846
DOUGLAS John Doncaster 22 69

Conclusion
If Harriet was a widow in 1851 - Charles wasn't born until 1853/54 so could not be her husbands child, therefore chances are he was illegitimate and hence the possibility his birth went unrecorded.

John married Harriet SAYLES in 1842. Harriet (daughter of Charles SAYLES and Sarah MASON) was born in 1822 in Doncaster, Yorkshire; died in 1903 in Rotherham, Yorkshire. [Group Sheet]

1. Charles Henry DOUGLAS was born about 1853 in Doncaster, Yorkshire; died on 15 Apr 1933 in Durham.