Puppylicking is used by Puppyshippers; people who ship Sirius Black/Remus Lupin of the Harry Potter books together, and is used in a loving manner, often between friends. One puppyshipper may puppylick a friend, but the friend, if not a puppyshipper, cannot puppylick back. It's most often used in the Fiction Alley Remus/Sirius ship threads.
Yvonne's fangirling the puppies was so cute, she just had to be puppylicked.
Anna gave Beth a puppylick.