I honestly think the only hope you have of finding the info is by getting a copy of his death certificate. It would also give the name of his parents, his birthdate, and where he was buried. It's cheaper if you order through the family search link:
http://www.bdm.nsw.gov.au/Pages/family-history/family-history.aspx You just need the registration number/year from the index, which is 3918/1868. It would also give a list of all his children, which might tell you things. If you don't want to pay for the certified copy, scroll to the bottom of that link, and it tells you how to contact them for just the facts on the registration, so probably much cheaper? This might be the way to go, as it very well not be your James. The Trove newspapers throw up multiple Allisons as a longstanding family in Dubbo.
On the 1841 and 1851 he is shown to be much younger than Agnes, so it's a guessing game so far as to his age.
There is a heritage report at
http://www.warrumbungle.nsw.gov.au/ArticleDocuments/684/CoolahShireHeritageStudyReport.pdf.aspx which has a couple mentions of the Oakey Creek Private cemetery, and that it is mainly Allisons in it. However, prior to James M Allison renting, then purchasing the land, it was owned by unrelated Allisons: two brothers named William and Mathew.
Source:
https://transcripts.sl.nsw.gov.au/page/369194/viewI have taken a look at online trees at various sites, and ran off screaming. Too many are just trying to guess which Allison goes where, with no proper documentation! (Things like James Sr dying in 1868, then being in the 1871 Scottish census.... or another where he was in Australia at the same time as serving in the American Civil war... *sigh*) However, one tree did have a copy of the death reg. for son Hugh, which indicated that his father, James Sr. was a gardener, if that helps.
Agnes (Mair) Allison was buried in Kunopia, which I think is a bit too far from Bundo to have her buried with her husband?
Going back to that heritage study: It looks like the Oakey Creek area where the private cemetery is owned by PasPaleygroup. It lists the cemetery in what they call Kurrajong Prk.
http://www.paspaleygroup.com/pastoral/kurrajong-park has contact info.
If you live close enough, perhaps they would allow you access to the private cemetery to take photos?
Anyways, I will dig around a bit more, but my instincts say you need his actual death registration to figure out his parents and where he is buried.