Tires were not available in metric sizes until about the 80's. It would have been either the old inch sizes (6.50x15) or more likely something like E78-15.
The repair manual for my '75 has these specs for the C10 tires:
4900 GVW - E78-15
5200 GVW - G78-15
5700 GVW - H78-15
When you look at these older tires, the letter (E, F, H) is a both load rating and size, so the tires get physically larger as the letters go up. The 78 refers to the aspect ratio (78%), and modern truck radials use a 75 aspect ratio. However, you can easily cross-reference the old size to a newer one of similar size. Based on this table, the P225/75R15 is the best match, but I would probably move up to a P235/75R15 because I like the look of larger tires on these pickups
http://www.vintagecarconnection.com/vintage_tire_size_conversion_chart.htm.
I use 245/75R16 on my K25, since it is a very common size for truck tires, and nearly the same diameter as my original tires (which were on 16.5" rims). It is about a 30.5"-31" diameter tire, and there is plenty of clearance in the wheel well. I think there is similar space in your C10, so you could also use a larger tire if you want to.
Bruce