http://www.carlgoldbergproducts.com/eagle2arf.htm
Sorry for the incorrect link. Here it is for the Eagle 2 ARF. It has the same engine information as the kit version. A 4 stroke would not be a problem.
I am installing a Saito .56 4 stroke in a Sig 4*40, and it was not nearly as easy as a 2 stroke would have been. I had to do a lot of thinking, posting here and modifications to make it work correctly. I had this engine on a stick beefore this and it is sweet!
Back to the 2 stroke engine... I have an OS .46 FX on a Sig LT-40. It is easily enough engine for this plane, and it is a bit larger then the Eagle 2. I would go with a light/small 2 stroke for the following reasons - 1. Better weight and balance 2. Better instalation.
But, I would also go with the Tiger 2 instead of the Eagle 2!
Good luck!