Headliner

The headliner on the t-tops of our 79 are coming loose.  Can someone please advise as to the best was to reattach.

The headliners are attatched with a combination of plastic "velcro" type pads, and small sheet metal brackets/screws. The problem will be whether or not the sub-structure of the headliner is damaged. It is made of a pressed/molded cardboard type material, and that stuff falls apart over the years.
You need to remove the headliners(called "T-Top pads"), and examine the back sides. If the basic pad is still in good shape, and not warped/damaged, you can simply use an epoxy to reinstall the loose "velcro" pads. Once they have dried, the pads should fit back in place with no drooping.
If the velcro pads have pulled the "cardboard" surface apart...you may need to replace the headliners.

Thanks, I had read that they were as you describe, but someone else said they were strictly glued together.  I am assuming you can just basically pull or pry apart.  Is this correct?

Well, yeah...after ya take the screws out of the side brackets/clips. I think there are only two clips with screws...look carefully first. After that, the pads just pop off. Chances are, if yours are hangin down the velcro pads will have pulled loose from the cardboard, or, on rare occations, the top itself.

OK, I think I follow that.  It's been awhile since I looked at them but it should be doable.