Up-sizing from the 1/2" to the 9/16" standard not such a great idea. Look at the crankarm, there is not much material there to work with. You may want to simply change out the arms, going with a three-piece bottom bracket. These use cups to down-size the shell to the 1.37" threading for the bottom bracket unit. Look for BMX conversion kits to do this, any good shop should be able to get you more information.

See also One-piece service

(On a technical note, tapping the 9/16" thread requires reaming or drilling of the hole. Use a 33/64-inch drill. The current size of the 1/2" threaded hole will be 29/64. Never use the tap to ream the hole.)