You can have Nikon fix your camera for a zillion dollars, or you can order a replacement part for half a zillion and attempt the repair yourself. Or, you can try one of the several do-it-yourself ideas that you find on the internet. The do-it-yourself ideas all seem to take one of two approaches:
- Repair the latch itself with some sort of microsurgery that involves gluing tiny pieces of metal or plastic inside the camera.
- Add a plate to the bottom of the camera that will press against the battery door and hold it shut from the outside.
The plate covers most of the bottom of the right-hand side of the camera. It's attached with a screw that fits into the camera's tripod mount. The plate then has a 1/4-20 tapped hole in it so the camera can still be used on a tripod with the plate in place. The slot in the screw is about the thickness of a penny, so all you need is a coin to remove and replace the plate in order to change the batteries.
The image below links to a PDF file with a detailed drawing of the plate and the screw. The drawing doesn't do a very good job of specifying the oddball curve on the right-hand side of the plate, but that's not very critical anyway and you can more or less just wing it if you decide to make a plate for your camera.
Note: The drawing specifies 5/8" for the diameter of the counterbore for the screw head. The counterbore really only needs to be slghtly larger than the screw head, as shown in the earlier photo.