Leahy was born in Creggane, outside Bruree, on the County Limerick-County Cork border, to Thomas Leahy and Mary McDonough.[2] He was one of seven brothers, all of whom were sportsmen. His brother Patrick won the British high jump record in 1898 and went on to win Olympic medals in 1900. Another brother, Timothy, also jumped competitively.[3]
In 1906, Leahy, Peter O'Connor and John Daly, were entered for the Intercalated Games in Athens by the Irish Amateur Athletic Association (IAAA) and Gaelic Athletic Association (GAA), representing Ireland.[citation needed] However, the rules of the games were changed so that only athletes nominated by National Olympic Committees were eligible. Ireland did not have an Olympic Committee, and the British Olympic Council claimed the three. On registering for the Games, Leahy and his fellow-athletes found that they were listed as United Kingdom, not Irish, team members.[8] Leahy was subsequently involved in the protest at the flag-raising ceremony for the long jump when O'Connor scaled a flagpole in the middle of the field and waved the Irish flag.[9] Leahy won the gold medal in the high jump with 1.775 meters, beating Hungarian Lajos Gönczy by 2.5 cm. After his victory was certain, Leahy still tried to reach 1.83 meters, but he failed at this height twice. Leahy then took part in the hop, step and jump, which O'Connor won with 14.075 meters with Leahy coming second with 13.98 meters.[citation needed]
In 1909 Con and Patrick Leahy emigrated to the United States. Con died in Manhattan in 1921. In 2006, to mark the 100th anniversary of his Olympic medal win, a memorial was unveiled in Thomas Street, Limerick.[11]