Use the GIMP, its an awesome image editor (and it handles gifs no problem).
If you want the picture you add to not move, just open the gif file in gimp, paste the image and before clicking anchor layer in the layer menu (which would only paste the image to the selected frame), click one of the two blank boxes (the one that when clicked, looks like a horizontal chain) on all of the layers in the layer/brush dialog box that appears on the left when you start gimp