Coccopalmerio was born in San Giuliano Milanese, Italy, where his parents were living during World War II, on 6 March 1938 and raised in Sernio, his mother's home town.
Coccopalmerio lahir di San Giuliano Milanese, Italia, dimana orangtuanya tinggal pada Perang Dunia II, pada 6 Maret 1938 dan dibesarkan di Sernio, kampung halaman ibunya sendiri.