This Christian Science Monitor article explains the history of the ingredients of a banana split:
"Bananas got to be big business in America not long after they were introduced at Philadelphia's Centennial Exposition of 1876. Bananas wrapped in tinfoil sold for 10 cents apiece. Soon merchants were establishing banana plantations in Central America and shipping the fruit to the United States. The United Fruit Company, which came to monopolize the banana business, grew so powerful that it virtually controlled the governments of some Latin American countries. (You've heard of a "banana republic"?) Part of the fruit's popularity was the fact that for a long time bananas, along with oranges, were the only fruits available in the winter."