Line a strainer with 4 layers of cheesecloth and place over a bowl. Place yogurt in prepared strainer; cover yogurt with edges of cheesecloth. Refrigerate for 8 hours or overnight.
Remove yogurt from cheesecloth and discard liquid from bowl. In a large bowl, combine the bananas, oranges, pineapple, marshmallows and coconut. Add yogurt; stir gently to combine. Cover and refrigerate for at least 1 hour before serving.