Speaking of "stamina" concerning piano playing is IMHO misleading.
What is needed is not power (like for running long distances or lifting weights), but suppleness of the body. If you want to compare piano playing to some sports, martial arts are most appropriate, because there not getting big muscles is important, but being supple and being able to direct one's energy exactly to the spot where one wants it. (Think of karateka easily striking through planks.)
And for suppleness, swimming is of course excellent when done without big ambitions and relaxedly. The whole body is involved, and the "reduction of gravity" helps to be able to move all body parts easily and freely.
I go swimming 2 times a week, and it's great! When I play immediately after swimming, I just fly over the keyboard and can feel how my playing will be in a few months by default :-)
A great exercise for helping arm weight playing: Stand in the water (the water must be so deep that it reaches your chest) and let your arms swim on the water. Let them completely loose so that the little waves transport them up and down and to the sides. Can you really let go so that they're swinging independently on the water?
At the same time monitor your breath (free flowing!), and don't stand rigid, but flexible.
Best Wishes,
Monk
Topic: felia