There's 3M Spray Adhesive which works great for carpet and headliner installation. I don't remember if comes with a needle or not. Usually when they droop what happens is the foam backing separates from the material making nice looking repairs pretty difficult to achieve.
FYI: Worst case scenario - if you need to replace the headliner; the cloth material sounds like what is very similar to what's in the Eagle's. It is foam backed headliner material that you can buy from most any of the larger fabric stores. It's available in a variety of colors and it's fairly inexpensive too, enough to do your Rebel won't bust a $20 bill. A lot of original AMC headliners have been replaced with the it.