I tweaked the original cover from sheshin but I expanded it to hide a 2Ah turnigy battery from hobby king and I included a mount for a micro usb breakout board for charging.
Update 2018-05-17: I'm happy with the shape of the cover as is, but I will be adding a third option soon for a USB C breakout board to charge via USB C. Additionally, I updated my pictures with the actual model hosted instead of an older one.
Update 2018-12-29: I decided I wasn't happy with the shape of the cover. I added a new lower profile version that should still fit the same cell. This requires cutting out even more of the original casing and removing the springs for the shoulder buttons. There is no room for an extra charge port so there is only one version.
These are the parts I used:
Warning: Completing this mod requires irreversible modification to the Gameboy Advance SP. You have to permanently remove portions of the lower housing to fit the battery snugly, even with the cover since the battery will sit at an angle. I recommend using an aftermarket housing. Soldering is REQUIRED.
You have to remove a large section of the internal battery tray on the lower housing near the cartridge connector. You must leave the other side intact otherwise the shoulder buttons will no longer install properly. After making physical room for the battery, I removed the battery connector from the motherboard and the JST connector from the battery and soldered the battery to the bare pads. Using a connector would be optimal but I have not yet found one that will fit properly and is skookum enough. I used hot glue on the soldered terminals to secure the wires. You can solder directly to the battery connector on the SP without removing it, but I opted to remove it since it will give me a little bit more room to work with and it will make the mod reversible as long as I replace the lower housing and do not lose the desoldered connector. Until final assembly, the battery should always remain disconnected from the circuit board to protect from shorts.
To add the Micro USB breakout board for charging, solder stranded wire (28 AWG is sufficient) to the VBUS and GND pads on the breakout board and connect the VBUS wire to pin 2 on the reverse of the power port and GND to pin 6. Make sure you use enough wire to maneuver the board through the hole made for the battery, around the battery and into the battery cover. I find that a service loop will give enough slack to maneuver the components and it will tuck neatly underneath the rear of the battery or to the right side. See pictures for more details.
I find that it's best to print the model upside-down and without any rafts to give you a smooth surface. My Maker Select v2 is relatively stock and had no issues printing this model with no support. You may need to slow down your printer to get the feet printed properly.
Originally I printed this model with PLA but I reprinted it with PETG. Either seems to work fine.
You'll have to add a screw to the printed model. If you purchased a new aftermarket shell for your SP, you can just use the new screw and the e-clip to hold it in (e-clip is not necessary) otherwise you can transfer the screw from your old battery cover as well.
Depending on your printer, some finishing work may be required but it is not necessary otherwise.