From Ripon registers
Gates 1827/08/06 c Gates Mary d Wm & Diana labr Ripon
Gates 1829/07/06 c Gates Jas s Wm & Dina labr Ripon
Gates 1831/08/30 b Gates Jas s Wm 2 Ripon
Gates 1831/11/27 c Gates Wm s Wm & Diana labr Ripon
Gates 1834/05/24 c Gates Jas s Wm & Diana bellman Ripon
Gates 1835/04/31 b Gates Wm s Wm [date sic] 3 Ripon
Gates 1836/04/11 c Gates Wm s Wm & Dinah bellman Ripon
Gates 1837/10/29 b Gates Wm s Wm 7m Ripon
Gates 1838/07/12 c Gates Eliz d Wm & Dinah labr Ripon
Gates 1848/03/17 b Gates Wm 49 Ripon
There is no marriage in Ripon for William and Diana\Dinah so need to look further afield.
1851 CensusLooking for a Elizabeth Gates born 1838 in Ripon gives this family. Note the mother is called Hannah but could this be Diana\Dinah changing her name. The Ripon records seem to indicate William dying in 1848. Note there is also a Charles born c1848, who are the true parents ? (not in the parish registers). The George Jackson seems to be a separate person in the household perhaps a lodger as Hannah was a pauper.
Hannah Gates 46 born St Mary Newington, Surry. Pauper
Elizaneth Gates 13 born Ripon
Charles Gates 3 born Ripon
George Jackson 47 born Easingwold, widower.
HO107/2281/156 p 8
1861 CensusCharles Gates 13 is with his mother now called Dinah Gates 55 born London (ie that is where St Mary Newington, Surrey is). I think her occupation is formerly milliner (?). I think this is enough to confirm the 1851 census is the right family. Therefore you could get the birth certificates of either Elizabeth or Charles to find Diana\Dinah’s maiden name (although an online tree claims it is Bleach). If so there is this marriage ie in(near) Diana’s home town
Name: William Gates
Spouse's Name: Diana Bleach
Event Date: 24 Nov 1825
Event Place: St. Mary'S, Lambeth, Surrey, England
https://familysearch.org/ark:/61903/1:1:N66B-P2Q1841 CensusNot found the family in 1841 but in 1851 they are at North Street, Ripon so you could see if someone could do a street search on that address in 1841 to see if they are there (maybe a long shot)