At any point, travel to Big Town on the map and speak to Buttercup about her dating Pappy. After that,, initiate the speech challenge with Pappy and keep on clicking the "Speech" option. Since it will never go away, you can just keep clicking it until you get the "Silver Tongued Devil" trophy. This trick works best if you speech is at least 30 to succeed in the Speech challenge. Note: This requires the unpatched version of the game.
Note: This can be done in the patched version of the game. Go to Little Lamplight at any point after you exit Vault 101 and get inside via Speech Challenge or rescuing other children from Paradise Falls. Go back to the "Great Chamber" and find Knock Knock to ask her how she got her name. Have her tell you a joke. She has only one joke and, with a decent Intelligence, you can interrupt it for a better ending. Then there is a Speech Challenge to convince her that it was a funny joke. Continuously cycle through the joke and Speech Challenge repeatedly. Because she is a child, the Speech challenge is also not too difficult.