Buy a cheap photo mat, put photo of the birthday girl or boy inside, and leave a felt pen or marker for guests to sign it. After the party, just add frame and you’ve got an instant bday keepsake.
This would also be fun for an older child’s birthday — especially if the guests are all just getting the hang of writing. Those first tentatively-written words are priceless. Use washable markers on a well-covered table, of course.