1909 advertisement for Firestone Non Skid tires
Clincher tires can be tough to mount sometimes. One thing that can cause trouble is when the tire sits unused in new condition for a few years. The tire “shrinks” somewhat, and it also gets hard. One enterprising Model T mechanic developed a solution years ago. We don’t know who he is, but thank you who ever you are or were!
The solution is to use a modern tire mounted to a wheel to stretch the old tire enough to make it easy to mount. In my case I am using a P18575R14 trailer wheel and tire. It is the spare from a two wheel utility trailer that I own. This tire when inflated to 50 PSI measures about 25 inches outside diameter at the center.
The process goes like this:
Deflate the modern tire. Make sure there is no tube inside the clincher tire. The clincher tire is then pulled onto the outside of the modern tire. Get it centered on the modern tire as much as possible. Inflate the modern tire to its maximum rated pressure. In our case the pressure was 50 PSI. 
Let the tire sit overnight.
The next day you can deflate the modern tire and remove the clincher. It will be much easier to install.