S.S. Orontes, The Australasian, Melbourne, 4 March 1905, p 13, http://nla.gov.au/nla.news-article140781270:

Fremantle, Thursday.—The Orient steamer Orontes arrived from London and ports after a fine trip this morning. Passengers:— [...] For Sydney— [...] Rev. J. Gilmartin [...]

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Churches, National Advocate, Bathurst, 14 April 1906, p 3, http://nla.gov.au/nla.news-article157293133:

Large congregations have attended S S Michael and John's Cathedral during Holy Week. The office of the Tenebrae commenced on Wednesday evening, and continued on Holy Thursday evening, when the preacher was the Rev Fr Gilmartin, C M, of St Stanislaus College. [...]

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Bathurst, Freeman's Journal, Sydney, 10 August 1911, p 30, http://nla.gov.au/nla.news-article111091589:

The Rev. Father Gilmartin, C.M., who during the past five years has been attached to the teaching staff of St. Stanislaus' College, has been transferred to the missionary staff of the Vincentian Order at St. Vincent's monastery, Ashfield. Father Gilmartin's fame as a gifted preacher is well known throughout this State, and in many other parts. On Saturday last he left for Cobar, where he will be engaged in missionary work for some time. [...]

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The Use of Vile Language, Manilla Express, 16 September 1911, p 2, http://nla.gov.au/nla.news-article195672746:

In the course of a sermon at St. Brigid's, Dubbo, Rev. Father Gilmartin, C.M., of Bathurst, scathingly condemned the all too common use of profane and obscene language. He urged his congregation to be missionaries for reform in this direction, and even advised them to take the law into their own hands when other measures failed. "I contend," he said, "that people who use bad language should be compelled to discontinue the habit, even if physical force has to be resorted to. If you are in the company of people who use filthy, vile language, you should tell them to drop it. If they don't do so, well, I advise you to drop them."

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Catholic Notes, Freeman's Journal, Sydney, 27 February 1913, p 29, http://nla.gov.au/nla.news-article108162308:

During the fifth week of Lent the annual retreat of the Sacred Heart Society will be held in the Cathedral by the Very Rev. Father Gilmartin, CM., and Father Donnelly. Masses will be at 6, 7, and 9 (children's), with instructions after the 6 and 7 o'clock Masses. Children will also receive instruction at 12 and 3.30 each day. There will be a special sermon at the evening devotions.

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Personal, Sydney Morning Herald, 9 July 1913, p 12, http://nla.gov.au/nla.news-article15434282:

The Rev. Father Gilmartin, C.M., for some years Professor of St. Stanislaus' College, Bathurst, and who has been more recently engaged in mission work, is returning to Ireland by the steamer Kleist, sailing to-day.

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T.W. Campbell, The Priests of the Diocese of Armidale: A Necrology, Braddon ACT, 2005:
Gilmartin, W

Listed in E J Doody, Acta et Statuta 1951, Appendix VI, Obituary List, in the section headed 'supplementary list of priests who have also worked in the diocese', but with no details other than the period he reputedly worked in the diocese, in this case 1911.
None of the available references list a priest by this name living and working in New South Wales at about this time. The source that resulted in Bishop Doody's listing is unknown. A Kevin Gilmartin CP is listed in MDHC records, but not in Southerwood. It is possible he is the same person and that, if so, he may have undertaken missions in the diocese during the period. He was not a priest of the diocese.
(Source: MDHC A-Z G44).

(Reproduced by permission of Tom Campbell.)