Long term fix and a customized look
If you have a few hours you can do it this way. I used to do custom van interiors part time back in the early 70's and used purpose built stuff but have found off the shelf replacments.
Stop at a fabric store and pick some fabric you like, buy enough to do the headliner, at the same store pick up some 1/4 or 1/2" foam sheet.
At an office supply store pickup a box of 'Brasstong round head fasteners, 1 1/2" long legs. 100 to a box for a buck or so. I use Charles Leonard Inc part number 6R-BP. Then hit a hardware store and pickup about 50 small washers that the fastners legs will fit thru.
Remove the headliner from the jeep, lay the headliner down on a large picnic table or workbench that you can walk around and strip off the old material, use double sided carpet tape to hold the foam in place on the headliner backer board, trim it with an electric knife at about a 45 degree angle along the edges.
Lay the material out so that it drapes over the edges about 2" or so..
Using a push drill pop a hole in the front center thru the material, backer board, folded over layer of material, put a brasstong thru, slip a washer over the legs, spread them then bend them back, the washer will keep the brass tong from being pulled back thru.
Next to the rear center, same thing, make the material snug, not tight. then do centers of each side, once you have the 4 sides done start filling in the rest. I usually work from the front to the rear. Once you have all 4 edges done put a few in the middle for support there, you can do a decoration or even spell 'JEEP' if you want to
Any holes that need to be cut for interior lights cut then in an X pattern then fold the tabs back and hot glue them to the backer board.
Tips:
You can paint the brass tongs any color to match or contrast the material.
Scotch Guard the material if it has not been done already. I have done a couple in urban and woodland camo and that stuff was already treated.
Fancy trim around interior lights can be done with aluminum flashing and can be cut into different shapes
You can also get medallions, like are used on saddles, from tack shops [place where they sell horse and riding stuff] and can put them infront of the brasstongs
Buy extra material to do the sunvisors, just sew it inside out and slide it over the sun visor like a sock.
If you have the patience and are willing pickup some sail thread at a marine supply store and a heavy sewing needle, instead of just filling the center with brastongs you can sew pleats in it for different effects.
If you want to put reading or map lights in the ceiling now is a good time to hit either an RV or Marine supply store for some aiming type map lights.
You can get a push drill at sears, looke like a screwdriver with different sized bits in the handle, used mostly to predrill molding for walls and doorways and such, works well for this too