Yes, there is a way to attach rubber to leather pouches that does not require string, if you are talking about tubular rubber.
Most mass-market tube slingshots use this method, and you can do it yourself at home as well.
It is detailed in Jack Koehler's book, "Slingshot Shooting." Pages 56 - 57. That is the procedure of burning a small hole in the tube, going through your pouch with the tube, and then running the tube back through the hole. This way is most common, I think.
Another method is even shown on pages 52 through 55. That way uses a piece of tube to attach the tube back to itself after it goes through the pouch. I didn't even know of this way until I read the book. Jack Koehler seems to prefer this way (figures 4-16 and 4-17) because it doesn't squeeze the pouch and bend the end.
Get the book from Jack at SUPERSHOOTING.COM. It's a must have for slingshot shooters.