 Nyorera kupfuurira kweiyi ndima - Munguva yake neRoma, Conti akakurumbira akapfeka hembe nhamba 7, uye akazova munhu akakosha nekirabhu parutivi rwerudyi, sezvo akahwina Scudetto mumwaka wa1982-83 uye Coppa Italia kashanu pakati pa1979 na1991. Akaita basa rinokosha mukubatsira Roma kusvika mufainari yeEuropean Cup ya1984, kwavakakundwa neLiverpool, naConti achirasikirwa nechirango chake mukutamba. Akabatsirawo Roma kusvika ku1991 UEFA Cup Final, mumwaka wake wekupedzisira nekirabhu, zvakare kuhwina Coppa Italia yake yekupedzisira mwaka iwoyo. 