There's the SAFE Network that will do exactly that. It's pay on put. You as a developer would have to pay a one time cost to store the app on network, but that should quite cheap. Users would then pay to store their own private data through the (web)app. It uses its own browser and protocol as sites are stored on a peer to peer network.

It's still in somewhat unstable test versions, but I think there's hope it can be out within the next year or so.