I've made dairy free ice cream frequently. Coconut milk, almond milk and pecan milk all turned out well. Also try fruit purees frozen. 3 cups of fruit puree to 1 cup of simple syrup. These are usually best eaten the same day you make them though if you add pureed banana, papaya or mango they seem to stay slightly softer.
Check Pinterest for the frozen banana ideas that kgraham mentioned. There are quite a few variations that work well.They taste amazing and the texture is really nice.
With all of our running and all of our cunning, If we couldn't laugh, we would all go insane...
"Changes in Attitude, Changes in Latitude" Jimmy Buffet