It sounds like you're looking for a genre of Christian Fiction with modern realism as a core component. Your request for "lighthearted" stories doesn't match what you're referring to, though. The Shack is about a man suffering from PTSD triggered on by the kidnapping, rape, and murder of his daughter. There is nothing remotely lighthearted about The Shack.
While there is a ton of Christian Fiction in print in the English-speaking markets, you'll find it in short supply in the web novel market, English-speaking or otherwise. There are a lot of reasons for this, but the primary one is that there is a very narrow range of popular genres and story archetypes in the web novel space at this time, primarily centered on what is trendy among young men in Korea, Japan, China, and Southeast Asia.
Personally, I think there is very little Christian Fiction that is well-written, but that's somewhat true for any genre. Part of the problem stems from a misguided notion among Christian writers that they need to force an agenda into a story, often in a way that is incongruous with the story itself.
If you are looking for recommendations, C.S. Lewis' Chronicles of Narnia is masterfully done. So are Madeleine L'Engle's Wrinkle in Time books. For a more contemporary author, Ted Dekker is passable, certainly better than William Young (who wrote The Shack).