Conflicting information on his religious order: OCD=Discalced Carmelite (A Prayer-Calendar of Deceased Priests & Deacons in Australia 1788-2009, compiled by W.T. Southerwood, Sixth Edition, 2009, p 97), or OFM=Franciscan (Fr T.J. Linane, From Abel to Zundolovich, Vol. 1, 1979, p 51).

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Possibly relevant: The Australian Church, Australasian Chronicle, Sydney, 29 January 1842, p 2, http://nla.gov.au/nla.news-article31734884:

We are happy to be able to inform our readers that the Catholic church in this colony has received another addition to the number of her pastors in the persons of the Rev. Mr. Coffey and the Rev. Mr. McEvey, who arrived yesterday by the ship Carthagenian, from Liverpool.

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The Banner of Belfast, Port Fairy, 4 August 1860, p 2, http://nla.gov.au/nla.news-article282199495:

At the Roman Catholic Presbytery, Belfast, on Thursday, 2nd instant, after a protracted illness, the Rev. Daniel McEvey, R.C.C. The funeral will leave the Presbytery this day, at one o'clock, and proceed to the Cemetery at Tower Hill.

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Death of the Rev. D. McEvey, R.C.C., The Banner of Belfast, Port Fairy, 4 August 1860, p 3, http://nla.gov.au/nla.news-article282199488:

It is with regret, we have to announce the death of the Rev. Mr. McEvey, which took place at the Roman Catholic Presbytery, at an early hour on Thursday morning. The deceased Clergyman entered on his missionary duties in Australia in 1839. About seventeen years ago, he accompanied the most Rev. Dr. Polding, and Dean McEnroe [McEncroe], from Sydney, on a mission to this District, and it is a strange coincidence, that though absent during a period of sixteen years, he was the first Roman Catholic Clergyman who officiated, and the first who died here. At an early age he left his native city, Dublin, for Spain, and completed his Collegiate course in the College of Salamanca. where he was ordained in the year 1837. Shortly after entering the priesthood, he returned to Dublin, and joined the mission in that city, being attached to Clarendon street Church. In 1839 he left Ireland, accompanied by other young clergymen, to join the Australian mission. After devoting a period of eight years to the zealous discharge of his missionary duties, his health failed him, and he was obliged to seek its amelioration by a visit to his native land, on his return to which he again became attached to Clarendon street Church; within the walls of which now historically celebrated edifice, the struggle for Catholic emancipation originated. In 1855 he returned to Australia, and was attached for the succeeding four years to St. Francis' Cathedral, where he designed and carried to successful completion, the beautiful building known as "Our Lady's Chapel" attached to the Cathedral. The magnificence of the interior of that building bears ample testimony to the exquisite taste, with which no doubt his continental experience inspired him. His health again failing, he was obliged to leave the scene of his labours, and was again about to visit his native country, but from the increasing duties of the mission, and the scarcity of clergymen, he was induced to remain in Victoria. He then proceeded to Geelong where he remained for a short time, from which place, at his own request he was removed to Belfast, in the hope that the comparative quiet of a country mission would restore his shattered health; but from the time of his arrival here he gradually sunk, until death terminated his sufferings. He was a man of capacious and highly cultivated intellect, and as an eloquent and impressive preacher, stood in the foremost rank. He died in the 46th year of his age, and the 23rd of his Ministry. May he rest in peace.