Get a high end blender. I use a Vitamix because the tamper works well with frozen foods whereas the Blendtec is not good for frozen foods.
Now what you want to do is use frozen fruits and blend them. Bananas frozen and peaches work well. Add to this a chilled but not frozen apple. You get good texture this way. You can also use things like oatmeal if you prefer a milkshake type drink.
Checkout your local Juice bar and see the flavors available. You can make these at home.
Ice Cream is not good food, it's sugar and fat. I wouldn't feed that to a child even if they could eat it. There are much better and healthy alternatives.