Since I do upholstery, I would suggest you do it this way. Get you some corrugated cardboard and make a template of your roof area you want to cover.
find some suitable 1/8th inch rods to use for boughs.
You will want to put boughs about every 12-16 inches front to rear.
Take your vinyl and sew tubes into it by doubling over the vinyl, making the tubes about 1/4 inch in diameter.
After you do this, lay your template out over the vinyl and mark it out for cutting, leave a little extra around the edges. If you are going to wind up with some sharp corners, I would hang the headliner using the boughs, and figure out where your fabric is going to have wrinkles in the corners. Gather it at those points and mark it on the backside so you can sew darts into it.
The alternative is to use your template to lay out a sheet of Samsonite or some compareable material, and using 3M or some good brand of spray glue, glue the vinyl to this head board.
This works great if you dont have a lot of complex curves to deal with. As you will notice, most production cars now use glued headliners to a stiff paperboad backing.
As for using screws, dont use them to attatch the fabric. Use a good stapler or # 6 uholstery tacks, and use an upholstery tack hammer to put them in, with a space not to exceed 1/4 inch between the tacks. Space staples even closer.
One more thing about using the hard head liner. Bring you vinyl over the back side of the hard board, about 2 inches, and glue those edges down as well. This will help in keeping it from puckering on the edges. Be sure to get the entire board covered with glue if you use the hard board way. Failure to do so will result in eventual bubbles which will cause the vinyl to start pulling away from the board and hang down. If you want to pad it, let me know. Directions for that as well.
Im not familiar with the vinyl that Restored60's mentioned. I use Marine grade vinyl in my work, as its more weather and wear resistant than conventional vinyl.
At any rate, get your vinyl from a professional upholsterer or supplier. One that has a non directional backing on it.