Frazer Manhattans used a 7.10 x 15 sized tire; the original type used on the production line were tube type tires. Previously, Goodyear tire stores were franchised for their line of vintage motor vehicle tires (and Goodyear was the main supplier to K-F for tires). The basic tires were blackwalls (the Goodyear is a whitewall) with whitewalls as an option. Note that current Goodyear production whitewall width is not the same as offered by the company back in 1947. If the Goodyear store in your area (and I am talking a factory store) can no longer offer the line, you will have to order through Universal, Coker, or some other vintage tire company listed in an old car magazine like HEMMINGS or OLD CARS WEEKLY. They have catalogs available and list various brands for this type of application.
Be advised that your wheels may not be compatable with the older type bias-ply tires, especially if radials are currently on your car.