If someone was trying to persuade you to do something, you might say “he spoke convincingly.”
What is a similar word for someone who is speaking in a way to gain sympathy from you?
Hope this makes sense.
They are speaking supplicatingly
= Beseechingly, imploringly; in supplication
From which, also consider:
Beseechingly, from beseeching : expressing or marked by earnest pleading or entreaty
“The wretched young man arose, and with a last beseeching glance at us walked from the room.”
in a way that expresses urgent or piteous pleading, as for aid or mercy; beseechingly:
“No! Don’t kill the spider!” gasped my daughter, looking imploringly into my eyes.