Conigliaro was born in Quilmes. As a player, he was a forward renowned for his technical ability. He played for many clubs in Argentina and abroad. His debut in Argentina was with Quilmes at the age of 15. He then played for Independiente, Chacarita Juniors, Estudiantes, Jalisco, K.S.V. Oudenaarde, Lugano, and Everton. In 1965, he arrived to Estudiantes de La Plata, who were a dominant force in Argentine and South American football during the late 1960s. During his time in Estudiantes, Conigliaro won three Copa Libertadores and the 1968 Intercontinental Cup. In the first game of the Intercontinental Cup, he scored the winning and only goal against Manchester United.