He was born in 1747, the first of two sons into a well-to-do farming family on the Castlecoote Estate. His father Daniel and younger brother John died when Daniel was still young. Daniel attended the local Hedge school at Briscula, just a few kilometres from his home. His mother, Elizabeth Delany sent him to her sisters, who had a shop in town, to gain a better education. As the public practice of Catholicism was outlawed by British Law at the time, in 1763, with the help of a good Protestant friend, the sixteen year old Delany was smuggled out of Ireland to Paris to study for the priesthood at the Irish College in Paris. He was ordained a priest in 1770. For the next five or six years Delany taught rhetoric at the English College at Saint-Omer in France. Father Delany returned to Ireland in 1776, disguised as a layman since priests were still outlawed. He was so appalled at the state of Ireland that he was tempted to return to France. However, his mother prevailed on him to stay in Ireland. Soon after arriving he was stationed at Tullow as assistant priest. Catholic education in Ireland had been denied to the people of Ireland since the seventeenth century; in consequence, much of the population suffered from poverty, hunger and drunkenness. Delany tried to bring back the traditional Catholic education to the community. He started by the establishment of Sunday schools for the youth of Tullow. He also formed a youth band to help teach his students hymns. Soon older people of the community started to join these classes.
Bishop
In April 1783 Delany was appointed Coadjutor to Bishop James Keeffe of the Diocese of Kildare and Leighlin, choosing as his motto Fortiter et Suaviter.
St. Patrick's College
With some relaxation of the Penal Laws in 1782, many Irish priests including Bishops Keeffe and Delany worked to rebuild churches, monasteries, convents and schools. In 1782 Keeffe and Delany began planning for the establishment of a tertiary college for the education of both lay students and those studying for the priesthood. St. Patrick's College was originally planned for Tullow but in the end, had to be situated in Carlow fifteen kilometres away. Keeffe died in 1787 but he was able to witness the beginning of construction. It was left to Bishop Delany and Fr Henry Staunton of Carlow to get the college finished. For financial reasons, it did not open until 1793, with Staunton as its first president. St. Patrick's, Carlow is the oldest surviving Catholic tertiary college in Ireland preceding St Patrick's College, Maynooth by two years. In 1784, Delany organized a procession through Tullow for the Feast of Corpus Christi. He also decided to start ringing the Angelus bell, which hadn't been done for a century. This caused some consternation, with Bishop Keeffe, concerned it would lead to trouble. With the death of Bishop Keeffe in 1787 Bishop Delany was appointed Bishop of Kildare and Leighlin on 17 February 1788. Sometime after 1794, his mother died, leaving him all her property. Delany invested a portion of this property left to him and the interest went to charities. Delany also distributed prayer books to children on the day of their first communion. He started a circulating library and was responsible for the building of a church in both Tullow and Mountrath. In 1807 Delany refounded the Congregation of St. Brigid, the Brigidine Sisters, and in 1808, the Congregation of The Brothers of St. Patrick in Tullow, County Carlow. In the convent gardens, Delany planted an oak sapling from Kildare. Today many of the Brigidine communities have an oak tree growing from the seed of an oak tree in Kildare. Bishop Delany died at two in the morning on 9 July 1814. He had been seriously ill for some months and was being cared for by the Brigidine Sisters in their convent. He is buried in his Tullow church.
The Delany Archive which holds the archives of the diocese of Kildare & Leighlin, the Patrician Brothers, Brigidine Sisters and Carlow College is located in Carlow College The Patrician Brothers in Sydney named the Delany Foundation and Delany Space after him.