GreatMartin asked about a dessert with coconut especially popular in the South, and this is how the Joy of Cooking describes this particular recipe:

"This is a versatile old favorite, especially popular in the South."

Ambrosia

Peel carefully, removing all membrane:
2 large Valencia oranges

Peel and cut into thin slices:
3 ripe bananas

Pineapple is sometimes added, as are other fruits.

Combine and stir:
1/4 cup confectioners sugar
1 1/2 cups shredded coconut

Arrange alternate layers of oranges and bananas in individual serving dishes or a bowl. Sprinkle each layer with part of the coconut mixture, reserving some for the top. Chill well before serving. Instead of coconut, try a garnish of: Crushed mint and a cherry or a strawberry.
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That's a fairly pure interpretation. Here is a more typical recipe from Allrecipes.com:

1 (11 ounce) can mandarin oranges, drained
1 (8 ounce) can crushed pineapple, drained
3 1/2 cups frozen whipped topping, thawed
2 cups shredded coconut
2 cups miniature marshmallows
1/2 cup milk
Maraschino cherries

In a large bowl, combine the oranges, pineapple, whipped topping, coconut, marshmallows and milk. Mix together well and chill 1 hour before serving. Garnish with cherries.