In short, yes, we document private cemeteries.
However, we will need some help of the Scotland Project on this one. I am not familiar enough with the area to create the correct category location name here.
For reference, the official name of the cemetery would be "Muiravonside House Graveyard" and have an AKA of "Stirling Family Graveyard." SMR 850 (Edwardian Conservation status) by the Falkirk Council.
There is a beautiful history of the House and Graveyard on the Falkirk Local History Society website.