For some reason I was thinking of a family bible from Scotland, not one created in New Zealand. It mentions Robina's place of birth as Stonehaven. This is the parish next to Fettersso and was a major fishing village / small town. I guess she could have been born in either parish.
Not much else to go on. As mentioned before you may never find confirmation of her parents. You could however follow up on the Chapman link.
Have you used ScotlandsPeople before. This is the official site for Scottish records. It is a pay site but has just undergone a major revamp (with a small price increase!!!). However, the main thing is searching is now free. Statutory Registration began in 1855.https://www.scotlandspeople.gov.uk/
For £7.50 you can get 30 credits which would give 5 BMD or census images. If you were to get the 1851 & 1861 census images you could confirm details. Add in the death certificates of Charles Chapman and his wife (you have the deaths from the grave details) which should give their parents and credits left for one further image.
The 1851 census image may or may not be interesting. The free index I viewed has her as a daughter of Charles. If this is a mis-index she may be shown as a grand daughter which would confirm the family connection. Also of interest is that SP has her indexed as Rebecca Chapman - this may be a mistake.
Finally if you like Charles Chapman as the grand father there may be a Will to view (or it may just be an Inventory of assets - the site doesn't say). The date shown is a few months after his death so it's probably him but without viewing the image you wouldn't know. The image costs 10 credits.