Hmmm..I had a problem with the diaries as well but it was slightly different to the one you are experiencing.
Basically diaries that I had picked up early in my game were physically missing from my wifes game when she began to play (on her own profile). Despite this they were listed as having been picked up by her in the diary menu page of her game, BUT the progress bar on the achievement wasn't registering or reflecting this. Other achievements with progress bars were also messed up for her.
I solved this by fully quitting the game, hard resetting the xone (hold power on button down for 10 secs), relaunching the game and then repeatedly reloading and quitting the current checkpoint. This caused the progress bar to progress a little at a time with each reload (see my post below for a more detailed explanation).
But if your diary is missing from the list and not appearing in game either for you to pick up then I am at a loss...
Only thing I can think of that might work is to totally uninstall/reinstall the game when you have finished everything else and replay again. You'll soon know if it's worked come the first diary pickup. I guess it depends where the data for your game is kept (local or cloud) and whether it's wiped when you uninstall.
Good luck getting it sorted it's frustrating I know.