Homemade Coconut Yogurt is Dairy Free – Hooray! - - Here’s a foolproof recipe for thick, luscious coconut yogurt. This recipe has a rich flavor and dense texture, almost like Greek yogurt. It’s Paleo, it’s vegan, it tastes great with fruit, and is easy to digest. Coconut yogurt is naturally sweeter than milk yogurt, so it doesn’t need sweetener. You can add a bit of raw honey if you like.