Because I’ve just recently discovered it: Coconut milk mixes surprisingly well with avocado. The latter is not particularly FP low, however, it doesn’t need much. When you shop for coconut milk make sure it lists almost no carbs and no fiber. You’ll find recipes easily on the web.
Keep in mind that typical, not too liquid smoothies like green smoothies often will have medium to high FP. When I started FTD I simply avoided smoothies, instead I was drinking tea and lemon water. But if you don’t mind the high calories of a coconut avocado smoothie or e.g. smoothies with whipped cream, these will have less carbs and less fiber.
One clever trick to get thick smoothies with low FP: Cook Jasmine rice for about double the time that it usually takes, so about 40-50 minutes. Put some into your smoothie and mix thoroughly.