We've tried dairy free pudding recipes before. We've tried ones with cornstarch and ones with tapioca powder for thickeners, we've tried ones with avocado and coconut milk/cream. We've skipped over the ones calling for bananas because our little guy's tummy doesn't agree with bananas, or we would have tried those too.
I gave up. I figured there is just something about pudding that cannot be recreated with excellence without the dairy protein. That's okay. We don't need to have a substitute recipe for every treat (especially the unhealthy ones) that we used to indulge in before we had dietary restrictions.
The next day, I took it out of the fridge, expecting to pour it into the ice cream maker, and discovered it was the most amazing pudding I had tasted in a LONG time. I have been able to add dairy back into my diet, so I can say that it didn't just taste good because I've been dairy-deprived (our taste buds do change as we go without certain foods, and that's a benefit, not a disadvantage! I find myself enjoying the sweetness of fruit and creaminess of avocados much more since I have been eating 'cleaner' most days.).
So, to make an amazing pudding, follow this recipe*, including straining the mixture for lumps prior to putting it in the fridge to chill: Vegan Chocolate Ice Cream. Then simply chill overnight and serve as pudding rather than putting in your ice cream maker.
*I used vanilla almond milk instead of soy milk, and I used Silk French Vanilla creamer as the nondairy creamer.
If you're looking for more vegan ice cream recipes, it sounds like you may want to check out the book The Vegan Scoop.