Cardboard Headliner

Well if you put vinyl on it (gluing) and for some reason over time it decides to start coming off then you could very well damage it. Vinyl is going to be heavier than cloth, and I have had my share of the cloth coming loose and start drooping. Riding with the windows open and air getting in and around it would accelerate the process.

That headliner looks in decent shape. If it were mine I'd paint it. Just my two cents...