I’ve had this problem with a few cars and I’ve never really found a way to fix it.
The ceilings always end up drooping and get pinned back up with embroidery pins. Is there a better way to fix this automotive malady that’s a bit more permanent?
The fabric headliner is attached (well, was attached) to a sort of cardboard backer (which give it shape) with an adhesive. The only permanent solution is to remove the backer, reapply adhesive, and re-adhere the headliner to it.
Here’s the bad news: on most cars, you have to remove the windshield or rear window to remove the headliner in one piece.
Staple gun
Drat! You beat me to it!
But that is the solution.
I fixed my car with wood trim, that Home Depot, and the like, sell.
They come in different lengths, 5-6 to 8 foot, maybe?, by 1/4-1/2 inch or so. Also, different patterns.
Take measuring tape, go from one metal trim above doors, to the other, being sure to push up against roof.
Add an inch for each end.
Length will vary as you move back in vehicle.
Use a grinder, hasp, whatever you have, and take off about half the wood from the inch on the ends on the back (unfinished) side.
The wood will bend enough that you can pop it up to the roof, and ends behind the trim.
May have to trim, or round off the ends.
Be careful not to pokes holes in fabric while doing this.
It took 5 strips for my car, and ended up looking like it belonged there, matching the trim on my dash.
I would think you could use different material strips… metal, plastic, patterns,…or paint them?
DUCT TAPE.
I have changed many headliners and never had to remove and glass to do it. Cars up to the mid 70s used spring rods to hold the head liner up. Gluing the headliner to cardboard then to the ceiling starting with the influx of Japanese cars in the 70’s. Headliners are not that hard to change. On a modern car, glue in the headliner/fabric panel using contact cement. Attach the liner to the tack strip around the edges, trim off the excess fabric and reinstall the trim pieces. It is one of those mystery jobs that is actually very easy to do. To fix a sagging headliner, I would buy some Scotch 77 spray adhesive, cut some access holes and spray in the adhesive. Then starting from the center, smooth the fabric to the ceiling. If the fabric has stretched, it may be necessary to retack the edges.
I stand corrected.
Where was all this advice when I was stapling my headliner up in my '84 Buick? 
Look in the yellow pages, there are plenty of guys that will go to your house and replace your headliner for only $125 -150
Headliners on the spot, is the one I use here in Atlanta