Last week I covered my ceiling with some very light weight indoor-outdoor carpet and used the water-based indoor-outdoor carpet adhesive to glue it up. First thing I did was cut a piece of 1/4" plywood about an inch wide and as long as the as the ceiling is wide and stapled it to the good side of the front edge of the carpet. I also made 3 "T" sticks out of 3/4" plywood to wedge between the floor and ceiling. I then screwed the plywood strip to the ceiling so the front edge of the carpet would be supported. Make sure the carpet is square with the roof or you'll end up with crooked carpet. After slathering on about 2 feet of the adhesive I found that the lightweight carpet would stick to the ceiling as long as the un-glued portion was supported with the T sticks. I would spread a section of the adhesive then move the T sticks back and press the carpet into the adhesive. Spreading the adhesive was the worst part of the job and I got it on most everything in sight.
Years ago I glued some heavier indoor carpeting on the ceiling of my van. The weight of that carpet would pull it away from the adhesive even with the T sticks holding it up so I ended up cutting a sheet of 1/4" plywood as wide as the ceiling and used the T sticks to press the plywood up against the carpet, holding it there overnight until the adhesive set up. Three T sticks worked nicely to evenly press the plywood against the ceiling. That method took way longer because I could only glue up one 4' section at a time but it worked fine.