This involves using the animation feature in Google Photos. The procedure is explained by Peggy K, a top contributor in the Blogger forum. You can find her post about this in Google+. She explains about using it in Blogger but as you can see it also works in Google Sites. You should view her detailed instructions but here is my condensed version:
To make a slower animation you can use an editor like LunaPic. You can upload your fast GIF, change the speed, save the image and upload it to Google Photos, get its URL and insert it into your page. (Don't forget to move it into a shared album)
See this example
Also see the image page .