Hi Mokki, I have seen one made from safflower oil and read about one made with coconut oil. Some Kroger grocery stores in my area carry the Hain's brand, but you may have to check at a health food store to find soy-free mayo.

I still buy it sometimes, but it really is pretty easy to make. I have even made it with bacon fat for a homemade version of Baconnaise. There are lots of recipes online, and if you have an immersion blender or food processor it really is pretty easy!