JR50 Mods/Upgrades ??

Find out how much "squeeze" you have between the top of the piston and the head. And I can do your machine work.

FMF makes a pipe for the JR50(part #023039) and JR80(023040), thats where Id start.

What are you looking to accomplish by this? If you want power just drop an .080 over piston in it. That will bring you up to 55cc's. Also yo can bore the carb out as it is really small. Get the FMF pipe.
Eliminate the injection by removing the drive gear and move to pre-mix.
If you need more bottom end you can unleash the "hidden" gear by elongating the slot in the shifter shaft making it a 2 speed. Then you can play with gearing via the sprokets and maybe get what your looking for???
Buy if you are trying to compete with the PW's and KTM OI'sin the injected class and want to stay legal just sell it and buy a different bike!

Based on my sons experience I found that the limiting factor on these bikes is the suspension more than the engine. In stock form the engine can get you into way more trouble than the suspension can get you out of. My son blew the rear shocks off of their mounts when jumping his JR. I agree with Jasle, the JR and bikes like it have their place in the evolution of the young dirt biker but your best move at this point may be to move to a more substantial bike. We moved to a Husky 50J that is made to be ridden like he wants to ride. He is way more happy with it. There are many more bikes like it out there that may be more suitable.