Using 'cajole' suggests a friendly, gentle method of persuasion, unlike 'manipulate' which is more negative. Her gentle smile could cajole anyone into helping her.
Pro Tip 2/3
Non-Forceful
'Cajole' implies persuasion without force or intimidation, but through pleasant means. He managed to cajole his sceptical friends into trying the new café.
Pro Tip 3/3
Subtly Persistent
'Cajole' entails a level of persistence; the speaker often has to sweet-talk persistently to convince. She would cajole her grandpa for stories every evening without fail.