Normally the drywall is put on the ceiling first and the drywall on the walls helps support it. In your case, I would use 5/8" drywall cut to fit inside the walls; in fact, allow 1/8" or so gap so you can get it in easier. Nail or screw it in place and you should be ok.
Read the drywall topic on my website at www.bobf.info for more help.