Sure. 'The Laughter Log' or 'The Joke Jungle'.
Here are some other ideas. 'The Mirthful Memoirs' - it's like you're writing memoirs of all the mirthful (funny) moments. 'The Hilariocity Hotspot' sounds like a place (your private story) where hilarity (funniness) is concentrated. And 'The Smiley - Story Sanctuary' gives the feeling that it's a safe place for all your smile - inducing stories.
Sure, how about 'The Cloaked Comedy' or 'The Masked Mirth'.
Sure. 'The Sneaky Snickers', 'The Covert Chuckles', 'The Private Puns'.
'Private Jokes Vault'. It's straightforward. It tells people that your private snap story is like a vault full of jokes that are only for a specific group or just for you.
Sure, 'The Hilarious Hideaway' or 'The Jolly Jokes Vault'.
Sure. 'The Stealthy Smiles' or 'The Quiet Quips'.
Sure. 'The Hush - Hush Histories', 'The Whispered Wonders' or 'The Secluded Stories'.
Sure. 'My Own Storybook', 'Solo Stories', 'Private Passages'.
Sure. 'Nocturnal Musings' is a good one. It makes you think of thoughts that happen in the dark of night, which can often be a bit on the darker side. 'Sable Narratives' also works, with'sable' meaning black or dark. 'Murky Reminiscences' gives the idea of memories that are a bit clouded and perhaps not so pleasant.
Yes, you could use 'The Endless Sadness', 'The Desolate Diary', or 'The Mournful Memoir'. The 'Endless Sadness' emphasizes the continuous nature of the depressing feelings in the story. 'The Desolate Diary' gives the sense of a personal account that is filled with emptiness and sorrow. 'The Mournful Memoir' is like a remembrance of things that are sad and perhaps lost. For instance, if the private story is about the loss of a loved one, 'The Mournful Memoir' would be a very fitting name as it encapsulates the act of mourning and the personal nature of the story.