Has anyone does a rechargeable GBP modification with any success? It sounds simple enough, (Li-ion Microusb charger with a hole drilled in the bottom to charge, with connection to the battery terminals). To keep it close to stock, I've thought of using AAA Li-ion batteries - would there be any issue with battery voltage/capacity? (The GBP is rated at 3v, but a pair of li-ion AAA batteries are 3.7v each).
The gb should be able too cope with the extra .7v. What your saying should work.. id use a lipo charging circuit and a soft cell 3.7v battery and maybe a 3v regulator but as I said the GB should handle that fine.. battery: http://ebay.to/1xV6Ack charger: http://ebay.to/1t5Mgji (pretty sure this will charge the battery off usb other than the other way around)
You would want to change the orientation of the cells too. The cells would be arranged in series in a stock gameboy to get the voltage above working voltage (3v). 10440 (AAA sized li-ion) would be 3.7v nominal, 4.2v fully charged, you are looking at 7.4-8.4v in stock cell arrangement. You could also look at lifepo4. It is a safer chemistry and lower voltage rechargeable that is typically rated for more recharge cycles. Its rated at 3.2v, but is 3.6v fully charged. Under load they drop quick to 3.2v. I would not be too worried about the extra voltage from a lifepo4 cell, though I would worry some about the extra voltage of normal li-ion and either chemistry cells in the stock series arrangement. Now for a charging circuit, you could check out either an ecig forum with a large modding community, like ECF, or maybe a rc hobby forum or a flashlight forum.