Hi,
If all of the covers are exactly the same size and the date will go in exactly the same place and will fit perfectly in the same place and the font and size will be the exact same size then this will be very easy to do.
First create a new document with the date on it, only the date as a solid color or whatever and the same color background as the cover, then merge all layers Ctrl+Shift+E, then select all, and copy to the clipboard.
Next, open up one of the covers and then open the actions palette and create a new action and start recording, then paste the date image and position in exactly the spot you want it to be, then save the image and close it, then stop recording the action.
Lastly, goto FILE > AUTOMATE > BATCH and choose the action that you just made and then choose the folder with all the covers and then let the process start, and it will paste the date into each cover and save and close it and it will do it to all of the images.
Hope this helps!
PS -
Save a backup of all the covers first - just in case, you never know
Hope this helps!