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.
I have a story about my neighbor. He was trying to paint his fence secretly at night so it would be a surprise for his wife. But he accidentally painted his dog's tail as well because the dog was sleeping there. His wife found it in the morning and couldn't stop laughing.
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.