Coleman's book, though written decades ago, is still one of the best sources for information on the early history of blasphemy in Australia. Chapter Four, "The Blasphemers", discusses a handful of prosecutions starting as early as 1871 and as recently as 1919.
The 1871 case involved the prosecution of a street preacher named Lorando Jones for giving a talk in a public park in which he denied the divinity of Christ and the divine inspiration of the Bible. Although Jones was convicted and spent some weeks in jail, Coleman states that "the case made the idea of prosecuting people for blasphemy so unpopular that it was largely responsible for finally killing the idea of blasphemy as a crime." (p. 65)
After a few pages devoted to the government campaign to suppress a freethinker magazine named Liberator (using laws other blasphemy, such as Sunday laws), the chapter goes on to discuss the Australian Post-Master General's vendetta against an Italian newspaper ("L'Asino") for publishing caricatures of God and a joint prosecution by the Post Office and the police in the State of Victoria against a Communist newspaper ("Ross's Magazine") for publishing a satire of what would happen if Bolsheviks took over Heaven. According to Coleman, this latter prosecution "is the last in which a Government instrumentality has taken action against a publication for its blasphemy." (p. 74)
I can't independently verify that statement, but no other cases have come to my attention either. Given the dearth of research on blasphemy laws in Australian history, Coleman's book is still worth tracking down.
* Note: This post is about the 1974 revised edition of the original 1963 book. I've seen some indications online that another edition was released in 2000 with slightly different subtitle.