Here's what I found on eBay: [http://www.ebay.com/sch/sis.html?_nkw=Nikon+COOLPIX+4600+5600+Battery+Chamber+Cover+Lid+Door|eBay parts listing]
Here's another link on getting the part directly from Nikon, they even sent them the needed instructions on how to replace the door! [http://www.fixya.com/support/t186242-replacing_battery_door_nikon_coolpix|Fitya - Coolpix 4600]
Here's the IFIXIT guide, sadly it only gets you part way there: [guide|9084|Removing Nikon Coolpix 4600 Front and Rear case]
Hope this helps! Good Luck