Hi Steven,
You can try using Overlay. e.g.
gif = Import["https://media.giphy.com/media/5UCpmbzvZKQCfuF2P2/giphy.gif"];
overlaid =
Overlay[{ExampleData[{"TestImage", "Moon"}], ImageResize[#, 200]},
Alignment -> Center] & /@ gif;
Export["overlaid.gif", overlaid]