An action would do it, but I am wondering about the 'exact same spot' requirement. Is that spot in relation to the bottom right corner, which is where watermarks often go? What about image size? I guess the images will be different sizes?
I'm having to guess here, but you might get best results setting the rulers to Percentage. Otherwise the action is probably going to reference the top left corner and place according to pixel dimensions, that will change one image to the next. Actions often tend to work better with rulers set to percentage.
We'd appreciate your feedback so we are better placed to help the next person to ask this. Thanks