Singing for me is not an option. Neither is dismounting. It would be more than a little rude to start singing, humming, or thinking about something either than what my coach is saying during a $100/hr lesson, let alone dismounting!
What has worked the best for me is kind of like meditating. If you think about it, our position on horse back is much like posturing on a yoga mat. Have a mantra for yourself to help you to relax by moving your body into a correct posture. Not only does focusing on something else help you relax, it really helps your equitation.
For me the biggest thing that helps is opening my chest by bringing my shoulders back and driving them to my hips. Then bringing my legs back from the hips and sitting into the saddle and "plugging in" to the horse. Another thing that is good for lower body tension is to softly bring the whole leg off the horse from the hip and bring it back down to rest again on the horse's side, hopefully in a better position.