Clerical Changes, The Irish Harp and Farmers' Herald, Adelaide, 1 June 1872, p 5, http://nla.gov.au/nla.news-article224364273:

[...] The Rev. R. Cleary from West Terrace to Mount Gambier. [...]

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Irish death record, https://www.irishgenealogy.ie/files/civil/deaths_returns/deaths_1881/06444/4851980.pdf: Superintendent Registrar's District Kilmallock, Registrar's District Kilfinane. 1881. Deaths Registered in the District of Kilfinane in the Union of Kilmallock in the County of Limerick. No. 366: On 7 March 1881 at Thomastown, death of Robert J. Cleary, male, bachelor, 34 years, Catholic Clergyman; of Hepatic Disease, 18 months, certified; informant: Mary J. Cleary, present at death, of Thomastown, 14 March 1881.

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Ballarat, The Age, Melbourne, 7 May 1881, p 5, http://nla.gov.au/nla.news-article204046831:

Our Ballarat correspondent, writing under yesterday's date, says : — Intelligence was received here last evening by telegram announcing the death of the Rev. Father Cleary, who was stationed in the Ballarat diocese previous to his visit to Ireland, where he died. The deceased gentleman was but 34 years of age, and was one of the most popular priests of the Roman Catholic Church during his residence in Ballarat. [...]

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Diocese of Ballarat, Advocate, Melbourne, 14 May 1881, p 8, http://nla.gov.au/nla.news-article170021657:

(From our own Correspondent.)
The news of the early death of the Rev. Father Cleary, which reached here last week, made a deep impression on many people, the late rev. gentleman being a very great favourite with all who knew him. He had a smile and a kind word for everybody, and he was indefatigable in the discharge of his duties. During the struggle to establish Catholic schools in this district, his energy might almost be said to have know no limitation. His death took place in Limerick, Ireland, on 7th March last. Though his demise would, of course, be a hard trial to his relatives and friends, yet, obviously, it must have been a source of consolation to them to be round his deathbed. His death was referred to in the various Catholic Churches throughout the Ballarat diocese on Monday. At St. Patrick's Cathedral, at the conclusion of the eleven o'clock service, the Benedictine clergyman, the Rev. D. F. Barry, who officiated, referred in pathetic terms to the demise of Father Cleary, whose place, he said, it would be hard to fill. The arduous labours which the deceased gentleman had encountered were touched upon, and the prayers of the congregation asked for the speedy admission of his soul into the kingdom of God. It was also announced by Father Barry that the Very Rev. Dr. Moore, V.G., had received a letter from the priest who attended Father Cleary on his deathbed, which stated that he passed quietly away, and with perfect resignation. Father Cleary, when in Ballarat, had charge of the Ballarat East presbytery, but shortly after his departure from the colony the undertaking was given to Dr. Hackett, who was succeeded by Father Meade. After Mass, and when the congregation were dispersing, the "Dead March" was played on the organ in an effective manner, the solemn notes of which served to remind those present that he, whose clear, ringing voice had been so often heard from the pulpit, and who was the life and soul in all charitable movements connected with the church, benevolent asylums, &c., was no more. In the evening, after Vespers, the Office for the dead was recited by members of the Christian Doctrine So- ciety for the repose of the soul of the deceased, the Rev. Father Sheridan officiating, and the members joining in the responses. On Monday, at half-past ten o'clock a.m., a solemn Requiem Mass was celebrated at St. Patrick's Cathedral for the repose of the soul of the deceased clergyman. The Very Rev. Dr. Moore, V.G., officiated as celebrant, and a number of the priests of the diocese took part in the celebration. There was a large congregation, all evidently deeply affected, their sadness bearing testimony to the bereavement they had sustained.

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Fr T.J. Linane, From Abel to Zundolovich, Vol. 2: Biographies of Priests on the Australian Scene up to 1900, 1980, p 50:

Cleary, Robert J., Irish
"A Kind Smile and Good Word for Everyone" ...
The late Fr. John Coughlin, Diocesan Archivist and P.P. of Horsham, was keenly interested in this young priest whose praises were sung in Ballarat and Irish papers on the occasion of his early demise. His brother, John J., first P.P. of Bungaree seems to be of a different mould. Robert was born in February 1846 at Kilfinane in County Limerick, being the son of Robert and Bridget (Moloney). Knowledge was imbibed at St. Mary's Clonmel and at All Hallows, Dublin. Ordination: 24 June 1870. Whether his lot was meant to be cast in Melbourne is not clear, but he arrived there on the 'Cardigan Castle' on 17 December 1870. Shortly after he arrived for duty in Adelaide he became involved in the maelstrom that had arisen in matters educational: the Mary McKillop — Fr.Tenison Woods issue that bedevilled the Adelaide Diocese for many a year. Misled by older clergy he signed a statement against the Josephite Sisters. Whether he and other signatories later on regretted their action is not clear. In 1873 a transfer was made to the Ballarat Diocese. He was among the small band of priests who were there to welcome the first Bishop, Dr. Michael O'Connor in December 1874. The following year he sponsored the opening of the 'Phoenix' School at Warrenheip, just east of Ballarat. Other chapel-schools in which he displayed an interest were at the Junction (Bungaree), Navigators, Dead Horse (Invermay), and at Fellmongers (Gong Gong). It was a crisis period for schools, yet one of great activity under the new Bishop — whose whole episcopal reign was devoted to opening new ones and preaching missions. In the late 70s Fr. Robert seems to have suffered a bout of ill-health, and decided to return to the 'old dart'. Following a farewell and many eulogies for his zealous activity and kindly personality, he departed to rest his bones in the place of his birth. Death took place on 7 March 1881 at the age of 35.
(Footprints, Vol. 2, No. 6)
Ref.: MDHC File, Torquay, per Late Fr. J.F. Coughlin, Horsham.