Well, kids' unique perspectives are often common in these stories. They see the world in a different way. For instance, a girl might confess that she didn't share her crayons with a boy because he had cooties. It's a childish view but it makes for a funny confession. Also, the interaction between the priest and the child is key. The priest's attempt to keep a straight face while the child is spouting all kinds of odd things is a common and funny part of these stories.
One common element is the misunderstanding of what a sin really is. Like in the story I mentioned before where the boy thought his siblings' normal behavior were sins. Another element could be the nervousness of the children. They often say the most unexpected things due to being nervous in that new and solemn situation. For example, a child might confess that they didn't like the way the church bells sounded which is not really a sin but just a random thought that comes out because of their jitters.
Often, there is the element of over - sharing. Children, not fully understanding the concept of confession, will just start talking about all kinds of things. They might start with a real sin like lying to their parents, but then go on to talk about how they don't like their vegetables or that they are scared of the dark. This over - sharing and the randomness of what they say is a typical part of first confession funny stories.