Does the ring that Edward gives Bella in eclipse show in the movie of eclipse?

Eclipse has not even been filmed yet, there is no telling what will be in the movie and what wont.

I believe so. The screenwriter said in an interview that she tought that the bedroom scene there was the most romantic scene in the book, and that she was excited that she got to write it. She said the most romantic thing in the whole saga was when Edward got down on one knee and proposed to Bella, and that she was excited to write that, so yes, the ring will probably be in the movie.

Yes, it will be in the movie.