Conrad was born in Manhattan, New York, and published his first song, "Down in Dear Old New Orleans", in 1912. Conrad produced the Broadway show The Honeymoon Express, starring Al Jolson, in 1913. By 1918, Conrad was writing and publishing with Henry Waterson (1873–1933). He co-composed "Margie" in 1920 with J. Russel Robinson and lyricist Benny Davis, which became his first major hit. He went on to compose hits that became standards, including:

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