I simply looked for him on census 1861 - found him and it showed Agnes as Cooper and unmarried.
No birth listed for William in name of Taylor so searched under Cooper (knowing she was unmarried in 1861) and there he was. There is also no marriage, as you'd already stated, between a Charles Taylor and Agnes Cooper.
As to tracing back Charles Taylor - now that really is a poser. His occupation, according to William's marriage certificate, is Pattern something - looks like Maker or Weaver.
Unless one is able to find something that seems to fit this you are kind of up a gum tree, so to speak. At this time, Agnes was born and living in Hamilton so one would suppose Charles was in that area too but cannot find anyone who seems to fit.
Annette