Take a look at pine resin epoxy if you wish to use an organic glue. It's a combination of pine sap that's slow boiled and then mixed with powdered charcoal. It will be brittle if you use too much charcoal, and weak if you use too little, but there is a sweet spot. It was used by the native Americans. I've played with it some and can confirm that the right mixture is indeed strong. Best thing about it is that you can get all ingredients in virtually any forest.
The glue is black in color. One would have to be careful in its application if the piece were to be of show quality.