Where I live, we have sour green mangoes. Many people like them for their sour flavor. 

I was trying to find a way to incorporate them into a cake, and I thought the best way would be as the icing. But I am not sure how best to do this.

So, I am looking for suggestions about how to make an icing based on a fruit -- and especially in a way that the sour flavor is not completely undone by the other ingredients in the icing.

A glaze, similar to a lemon glaze, would be an acceptable second choice.

Thanks much in advance!

How about making a fruit curd? I have never tried mango but passion fruit is a charm. You have to give a lot of trial and error to get the right consistency. I'll use it inside of the cake to preserve the flavor. Keep in mind that nay fruit cooked or raw will be susceptible to spoilage. 

My thought was exactly the same, a curd or even a puree used as a filling between the layers.

yes or perhaps a coulis that you can marble though the cake batter before baking -- maybe add an apple before cooking the coulis