Have you checked Bdm.nsw.gov.au for the death registration of William? It should give you the first names of his parents. If he died in 1961 you would need to be a family member to get the certificate. Earlier registrations however are all online.
the ryerson index is also a good site for recent Australian deaths. Ryersonindex.org
i found this one, not sure if it is him, it is the closest to Bundarra. There were others
Surname Given Names Notice Type Date Type Age Other Details Publication Published
ROBERTS William Funeral notice 31OCT1961 Funeral late of Cubawee, Tuncester Northern Star (Lismore) 30OCT1961