Liverwort is, biologically, the same as moss, so mosskiller will work on it. DIY places sell stuff to spray on paving to kill moss and algae. In my experience, they work. It's not a permanent solution though, it grows back after a while, and in conditions particularly favourable for their growth, it can grow back very quickly. I treated my paving in May this year, and such has been the the cool damp summer this year that in the more shaded areas it is already growing back strongly. Usually it waits until winter...