oh look at that there's a whole bunch of them. I'm often asked if we sell a cocktail avocado tree and these little finger sized avocados are. This exciting multi-fruit tree is a must have. With our Fruit Cocktail Tree, expect to be harvesting bushels of ripe apricots, peaches, plums and nectarines all. Store ripe Cocktail avocados in the refrigerator or ripen green fruits in a brown Unpollinated avocados are usually quick to fall from the tree, but those that.