Some great funny names for private stories could be 'The Exclusive Escapades'. This name makes it seem like the story is something only a select few can know about and is full of adventures that are also quite humorous. 'The Clandestine Comedy' is another good choice. It clearly states that it's a comedy but also something that is hidden or private. You could also go for 'The Hushed-up Humor' which gives the sense that the humor in the story is something that is not widely known or shared, but rather kept quiet and private.
You can also play with words. If your story has something to do with a rainy day, instead of just 'A Rainy Day', you could call it 'The Rainy Day Rhapsody'. Or if it's about a broken chair, 'The Chair - A Tale of Broken Dreams'. Look at the main elements of your story and give them a humorous or over - the - top spin.
Some good ones could be 'Confidential Chuckles', 'Exclusive Escapades' and 'Restricted Ridiculousness'. These names give a sense of secrecy and fun at the same time. They can make your private stories seem more interesting and unique. For example, 'Confidential Chuckles' implies that there are some really funny and private things that only a selected few can see, which is exactly what a snap private story is all about.