Here is a gif to show you a simple animated busy.org logo on my cover image.
First things first, my cover image is not a gif. I'm not sure if we can have a gif as a cover image, I haven't tried. I'll leave this task for you guys to try out. My cover image is an SVG file. SVG stands for Scalable Vector Graphics. Here is the SVG page from Wikipedia. I won't say too much about SVG but I just want to point out that SVG can be altered with CSS. Since you can animate elements on a web page with CSS, we can animate SVG as well.
Here is the svg file ( hope it works in the post)
I host my svg cover image at svgur.com . A pretty basic hosting service for svg files that is free and offer direct link.
The cover image works on busy.org but is not working on steemit.com . That's the first thing I've noticed but I'm sure there are other things that will break my cover image. I leave that to you to discover and let me know in the comments what you found.
I'm sure it works on Chrome browser if you want to have a look :)
It works on my Android phone using chrome browser though the logo is almost of the screen to the right.
That can be fixed with some CSS positioning witch is beyond my knowledge for now, just a noob here 馃榿