One possible solution is find(1)'s -(a|c)newer flags. For that you need to know the last file created/accessed. Then use that file to find the latest ones. You could also use a default file, perhaps a hidden file, and use touch(1) to update the access time of this file everytime there's a new file.

Inorder to get the name of a deleted file, you'll prolly have to save the filenames somewhere. And then compare this list with the current filenames in the directory.