Have you seen +Scott Malthouse's solo RPG game Quill? In essence, it is a letter writing game, where you take on the role of a character trying to convince a distant NPC to undertake some action, and you score points based on attribute rolls and how many specific words supplied in each scenario you include in the letter. Here's how Scott puts it in the intro to the game:
In a typical game of Quill the aim is to impress your recipient into responding favourably to your letter. You will accomplish this through deft use of language and presentation, rolling dice to determine whether or not you succeed in using the right words, the best descriptors and the most beautiful penmanship. Once you have completed your letter – one which you will actually physically write yourself – you will count up your total score and discover how your letter has been received.It's a neat little game that is both a creative writing exercise and a clever way to create plot seeds or adventure hooks for other games. There are four scenarios presented in the main rulebook (which is only 16 pages long). On Valentines Day, Scott released a supplement called Love Letters which contains an additional 5 scenarios to test your persuasive abilities.
You can find some examples of actual play here at the Quill Roleplaying Society G+ Community.
And here, I offer 2 homebrew scenarios of my own design: