Scratch

Or, you can ask somebody to make you one by looking in the Requests forum section or posting a request there 

Here's a good guide by Bluestribute

Flash is a bit too professional, but if you have access to it, it'd be brilliant, also, serif draw pro 8 or higher have animation tools on size presets specially for things like this. The only problem is making them a gif......

You can get one a few ways.
1.) Making it yourself. (All I do is make multiple frames, then I save those frames separately in a folder, and go to a .gif generator website and then save the new image. There's got to be another way to do that with an easier process though.  )

2.) You can you in the Requests Forum and make a topic asking that you want an animated profile icon (It makes it easier if you specify what you want.) Or you could go to other users "shops", but make sure that profile pictures are what they make. (Again, it'd be easier to specify what you want.)

3.) Find one that you like from google or such (Say a mario or sonic .gif). The only flaw about that is the fact that its limited of what you can find, if you ask another user or make it yourself, it's a little, let's say "custom".

I hope this helps, and Scratch on!

He/she is called awesome studios for a reason!