Hi Tom
Wozzle's possible 1861 looks promising, although I am not seeing the birth of daughter Margaret on SP easily. Could be that she was born in Ireland and perhaps birth place wrongly recorded

I see from the Antrim board that John and Rachel's marriage entry has him recorded as William John which adds to the possibility of that 1861 entry in Paisley, also the occupation would fit.
There is a submitted entry on IGI for births. It's seems too early, but I thought the mother's name was interesting:
WM DOUGLASS Christening: 10 NOV 1822 at St Annes Parish, Belfast, Antrim
Parents: JAMES DOUGLASS and LEAH SPENCE
You say you have managed to trace Rachel back to her family. What were her parents's names - just trying to see whether there is anything to be seen (guessed at this stage!) from the names they used for their children.
Monica