There is a specialty adhesive used just for headliners made by 3M - you should be able to find it at JCW. You can also check local body shop supply outfits, and some of the better-stocked "small" local parts houses might also have it.
Make sure the backing board is clean - I believe there's usually a thin layer of foam under the fabric, and that should be scraped off before you try to reapply.
Some also report good results with putting polyester resin (part of a fibreglas kit, available pretty much anywhere) on the top side of the board to reinforce it.
I've also heard of people using some variety of brads or carpet tacks to help the adhesive out - push through from the cabin side, and bend the prong over once the head is snug against the board. This would be difficult if you've already coated the board with resin, but you can get it all done up, and then coat the board afterwards.
NB - If you use some variety of anything that might shrink, wash it to shrink it before you stick it on the board! Hell, wash whatever it is first anyhow, even if it's new. At least knock the sizing out of the stuff...
Also, if you reinforce the board with polyester resin and do a very good job of cleaning the inside, there's no real reason whatever you can't just paint the inside of the board and eliminate the fabric from the off.
NB - If you paint and/or use resin, allow a minimum of one full week for the thing to outgas in the garage before you install it back into your rig. No sense risking passing out behind the wheel, is there?
