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.
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.
Sure, how about 'The Cloaked Comedy' or 'The Masked Mirth'.
Sure. 'The Sneaky Snickers', 'The Covert Chuckles', 'The Private Puns'.
Sure. 'The Laughter Log' or 'The Joke Jungle'.
You might consider 'Veiled Vignettes'. Vignettes are short, descriptive scenes or stories, and the 'veiled' part makes it private. 'Privy Perspectives' is also a good choice as it implies a perspective that is private or known only to a few. 'Reserved Recounts' gives the sense that these are stories that are reserved or held back, which is perfect for a private story.
'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.
How about 'Faith's Hidden Tales' and 'Grace - Laden Lore'. These names convey the religious aspect as well as the privacy of the stories. 'Faith's Hidden Tales' emphasizes that these are tales related to faith but are hidden or private. 'Grace - Laden Lore' gives the sense that the stories are full of grace, which is an important concept in Christianity.
Sure, 'The Hilarious Hideaway' or 'The Jolly Jokes Vault'.