Ah, the Road Puppy, my favorite name for a bicycle. Back in the mid 1970s, when I was working in a bicycle shop, a Shriner's clown brought one of these into the shop to get new tires. The ones on the bike had duct tape wound around what was left of the tires. After unspooling the tape, I managed to get one of the tires off to get a look at it. It was, I learned, an old fashion "clincher tire". Not only did it have a wire bead on each side but extending from each wire bead was a flap that acted as a rim strip. We consulted with our suppliers, including District Cycle of Greenbelt, MD. Most had never seen that type of tire, except for District Cycle. Needless to say, that kind of tire was not available in the USA. This was eons before the internet, so a search outside the USA was out of the question. Now today, I'd suggest you do a search on the Ebay of various countries, including the UK and Japan.
Many of the early Road Puppies were brought back to the US by service men returning from being posted in Japan after WWII. That bike that I worked on had "Made In Occupied Japan" written on the head badge. The bike continued in production for quite a few years after that, with upgrades made to the brakes and wheels, which went to a more modern tire (no flaps). I will contact a friend who has a large collection of all kinds of bikes and see if he has any info/ideas.