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do gymnastics(there are a lot of fitness centers who do this for kids who are 2 and above), that is a GREAT way to get rid of his energy! :)
i would say soccer. you could check out your local ymca. if you have a gymboree near by, they have a "sports" class but i want to say its for 3-5 year olds. it might be for 2-5 but i cant remember. good luck!
karate is out until he's atleast 4 or 5. that's the earliest any karate instructor will take him. call around about a tumbling class.
Organized sports are for older children, generally kids have to be potty trained before being able to join classes or sports. Activities and lessons for children generally start at age 3.
Two years old is too young for organized sports. The body of a two year old isn't built for the rigors of a sport and they can't truly understand the game. If you want him doing something active you should just take him somewhere he can explore or run and jump and play with other children. Or, like someone else said a gymboree place that's not yet a true "sport" but it's active.