Which sport would improve coordination: tennis, archery, bicycling, or swimming

To answer your question archery AND tennis would help improve coordination.

All of the given activities will help improve coordination.  Each would work on a very specific set of muscle group coordination, but all involve very specific technique required to master the activity.  As one practices in each of the activities there is generally improvement as the coordination and muscle memory improve and become more automatic.

Try tylenol or see a professional