I'm always nervous of degrading the adhesive on headliners, so I'd start mild and work up from there as needed:
Start with mild cleaner such as Woolite 6:1, then try APC 10:1, then reduced pressure steam.
Don't soak the headliner, but apply the cleaner to a MF and then wipe the headliner.
I've removed soda can spray with good success using these methods.
Good luck.