The only recorded historical event to take place during Eärendil's reign came three years after his accession, when Elrond's daughter Arwen was born in the north. No-one in Gondor at that time, of course, could have known how significant that event would be: nearly three thousand years later, Arwen was to wed Aragorn, a distant descendant of Eärendil's ancestor Elendil, and become Queen of his realm.
Eärendil ruled Gondor for eighty-six years, and was succeeded by his son, Anardil.
The date of Eärendil's birth appears only in The History of Middle-earth volume XII, The Peoples of Middle-earth. It cannot therefore be considered completely reliable.