I bought the Riley last year, and I was warned pretty early by the Riley community that the vinyl roof is not decorative. The metal under it is not solid, and water will go right through if it leaks. When I first got the car, I treated the roof with a waterproof coating in hopes that it would help, it didn't. I just don't go far if I think it might rain, and always keep a cover in the trunk. 
The Riley club in England sells a replacement cover, but it cost's over 300 pounds not including shipping. Being the cheapskate I am, I figured it was worth seeing if I could make my own. We already have a sewing machine hanging around that we don't use, so I figured it was worth a try. I bought some vinyl and got the biggest needle and the heaviest thread that would work in my machine, and it sewed like a champ. 
That is what is referred to as a full flat felled seam, it is supposed to be the strongest and most water tight seam you can make. I also learned about what is called basting tape, which is essentially just double sided tape that you stick the fabric pieces together with before sewing. It is supposed to help make sure the joint is waterproof, I figured anything would help.
I took over my entire dining room for about 3 days while I put this together and sewed it over and over. I ruined the first attempt when it folded over itself on the way through the machine. luckily I bought a huge amount of material because I wanted some extra, and I misunderstood how fabric is sold. 
I managed to finish the sewing without any huge screw ups. The seams aren't super straight, and the texture isn't exactly right, but it should keep the inside dry.
Part two:
Time to start removing the old roof. It is secured by a piece of aluminum trim with a rubber gutter insert that runs the perimeter of the roof. 
After taking out the insert, you can see the nails that secure them. After pulling those nails and taking the trim off, you find a lot more nails.
After you pull all the little upholstery tacks out, you can finally take the cover off. Under the cover you will find a layer of burlap fabric, and a layer of batting under that to smooth the whole thing out.
I guess I'm not a purest as I'd weld a steel roof in place of the fabric. Never could understand the reasoning for fabric roofs if they aren't a convertible.
Nice to see a RM Riley on here. 
Nice job so far. Good luck with the fit.
I believe the wood work around the rear screen is problematic. Having dealt with leaks, I suggest you have a close look for rot.
B
In reply to riley1489 :
It's actually really solid. I was quite happy to see the condition of it.
So what do the nails go into? Is there wood backing under the metal roof area?
There is one of these cars listed locally in a bit worse shape than yours. It's all there but pretty rusty.
I will say they are nice looking cars.
In reply to brad131a4 (Forum Supporter) :
This is what it would look like if I peeled the metal off. It's what the british call wood framed.
This is the roof above one of the doors. The body has a nail flange all the way around. The roof and the trim nail in those gaps between the body nails. I spent the afternoon filling every hole with wood filler around the entire perimeter.
This is above the windshield. The steel has oval holes punched out so you can nail into the wood below.
@rustyvw
These are lovely cars and a delight to the eye.
Sadly the Riley Motor company thought building under powered timber frame cars post war and thinking America would love them was folly.
Nice job on the roof best of luck finishing this off.
B
