Flarfball: Objects Lesson
These are the objects of Flarfball. As you can see, the parts are clearly identified as having certain dimensions which stay the same over the course of the animation. Animate the bouncy element underneath the trampoline after drawing all of the other action, accounting for the "sinking" feature of the person that is bouncing on it (indicated by the indentation to the underside of the trampoline).
Also mentioned in this page is the concept of the circlehead. That's a method of drawing characters that involves drawing a circle, which is the head of the character, drawn as the first layer. It becomes a reference point to the location and position of that character, as it changes throughout all of the animation's frames. The additional parts to the circle are what make it into a character, and not just a circle, but those can be added later once that "layer" of the circlehead has been drawn.
That's a technique that can help you out with yours.