[Pyrotechnic]

I looked into headliner re-gluing and the main concern is the ability of the adhesive to last through heat and time. Use a weak contact cement and you do a lot of work for nothing. From what I could gather, the best two contact cements are:

DAP Weldwood with a red label, available at home depot, lowes, etc. You can brush it on. This is the flammable stuff with all the good chemicals in it. Apparently the water based with the green label doesn't work as well.

DAP Weldwood Landau Top and Trim. This is industrial stuff, meant to be used in a spray gun and it's what an upholstery or convertible top shop would use. I read this was the best, but probably have to be ordered from a industrial supplier.

Either way, try a small bit of glue on a hidden spot to make sure it doesn't react badly with the vinyl.