Is there an alternative to using oil when baking muffins I make a lot of muffins and I am constantly altering the recipes to try and create the perfect muffin to satisfy my taste and keep me regular.  

I also avoid using sugar and oil.  

I have been substituting unsweetened applesauce (equal part) for the oil; and I just read a great response on this forum regarding the role that oil/applesauce plays in baking (very informative, thank you!). 

I'm wondering if there is an alternative to oil/butter/margarine/lard/vegan butter, etc. that will give me the taste and consistency that I would get had I used the fat called for.

Editorial:
I am not looking for a substitute for the sugar.....There are many ways to add sweetness to the recipe.  The article I mentioned above (role of oil in baking) explained that the fat protects the flour from becoming to glutenous (or chewy) in the baking process.  It further explained that the pectin in applesauce has the same (albeit diminished) affect on flour as does the oil.  However, it said that this is where the comparison stops ~ implying that there are other desired effects from oil in the baking process.

I know from eating my muffins that there is something different about them than had I used oil.  I just can't put my finger on what it is (it is more in the consistency than in the taste). And so I am wondering if there is some ingredient I could add, perhaps in addition to the applesauce, that would make up for whatever else the oil is good for that is missing from my muffins.

Thanks.
Yoghurt, squashes, yams, sweet potatoes, egg yolks, tofu or ground nuts could possible be added as an alternative.