Antonios (often Antonakis) Triantafyllides was born on 26 January 1890 to a Cypriot family with prominent and significant public service dating from the late Ottoman period and his family became prominent Cypriots too. His father was Michalakis and his grandfather, and namesake, born in Beirut, had been instrumental in removing Archbishop Panaretos for abuse of power in 1840 and was a member of deputations to Constantinople (1840, 1856 and 1870), with that in 1856 obtaining administrative reforms from the Porte. Antonakis was educated in Nicosia, studied law at the University of Athens (1907–11) and returned to Nicosia and established in July 1912 what became one of the finest law firms in Cyprus.

His three sons were all prominent Cypriots. His eldest, Michalakis (1927–2005), had represented EOKA members before the courts, and was considered, even at 28 when EOKA started by Charles Foley, a British journalist sympathetic to EOKA, as ‘one of the most brilliant lawyers’ in Cyprus. Michalakis was a member of the Constitutional Commission (1959–60) that drew up the constitution, was appointed judge of the Supreme Constitutional Court when Cyprus became independent in 1960, was made a judge of the Supreme Court in 1964, before being appointed president of the Supreme Court in 1971 and Attorney General in 1988 by President George Vassiliou and his successor, President Glafkos Clerides, until Michalakis retired in 1995. In 1974, when the Greek Junta ordered the coup against President Archbishop Makarios III, Nicos Sampson, a former EOKA gunman and later paramilitary leader, who became the president of the coup, was ordered to find Michalakis Triantafyllides to be the president. Triantafyllides was overseas, but is unlikely to have accepted, since the Junta wanted him only to give legitimacy to the coup. His second son, Solon (b. 1932; d. 2016), was an accountant, the first president of the Institute of Certified Public Accountants of Cyprus in 1961, and the long-time chairman of the Bank of Cyprus, 1988–2005 (Antonios was on the board when he died). During his chairmanship, the Bank of Cyprus grew, he invested more in its Cultural Foundation, and established the Bank of Cyprus Oncology Centre.