That's what I would like to know, too (although this wouldn't be the first JCS-related thing I should've known about but didn't for whatever reason). I have no idea how to insert a new animation between other animations, but I have the next best thing and it's fairly simple.

All you have to do is clone all of your current animations in the correct order by pressing C on each animation. After you do that, delete all of the original animations except for one, which you will use to replace the animation you deleted. Just make sure you don't accidently delete all the tiles in that animation while you change around the tiles. That's all you need to do.