I've done a headliner replacement my self. Did it on my '87 bonnie then the next week i did it on my cousin'* beretta. I couldn't find the 'right' glue for my car but we found it when we did it on his. He has NO problems with sagging of ANY kind. looks like BRAND NEW.
The glue is readily available at auto parts stores, it'* 3M brand and it'* called automtive trim adhesive, there are two types, buy the most expensive kind, it is the same color as the yellow contact cement you might usually buy at a hardware store. Of course this is a spray, not a brush on glue. This glue is the best for headliner application. Spray liberally, just dont get big clumpy puddles of it -- that has a chance of seeping through the foam and to the top layer.
Also: you can tell you're getting the right one because it costs about $12 - $16. If it costs $7.00, you're not getting a 'good deal' you're getting the wrong product (that would be the 3m brand spray that I used.. .and now the back area istrying to sag .... of coures this isn't the same 'sag' that one is used to with a headliner because that is due to the top layer coming appart from the foam backing, my 'sag' is the foam backing coming off the fiberglass ceiling plate thing.
if i had pics of my car i'd post em :(