The 1841 census lists the Davidson family at Balnoe: John, 35; Jane, 30; Duncan, 8; Jane, 2 and Ann Ritchie, 9. Jane Farquharson or Davidson, mother's surname Ogg, died in Glenmuick Tullich and Glengairn in 1873 aged 74. John Davidson, mother's surname Davidson, died in Glenmuick etc in 1887, aged 84.
Realistically your best hope for finding out the names of any earlier occupants would be to hope that the rental records of the estate have survived. Start at
https://www.nrscotland.gov.uk/research/catalogues-and-indexesAccording to the 1855 Valuation Roll the proprietor of Balno was the Marquis of Huntly (and the tenant was John Davidson). This is confirmed by the Ordnance Survey Name Book
http://www.rootschat.com/links/01sp3/ You could also go through the whole of the parish register noting any mentions of people in Baln/Belnoe etc.
The simplest way to do this would be to go to a library where the relevant register is available on microfilm - Aberdeen Public Library should have it, as should the Aberdeen and North-east Scotland Family History Society and the North-East Scotland Library Services HQ in Old Meldrum. There may be others. Or book a day in a Scotland's People Centre.
If you aren't in Scotland and cannot get to any of these places, you will either need to hire a professional searcher - see
https://www.asgra.co.uk/ - or go to your nearest LDS Church Family History Centre and arrange to rent the microfilm to be viewed there.
Or you could download all of the parish register at £1.50 per page from
www.scotlandspeople.gov.uk - the easiest of all, but more expensive.
