I'm looking to replace several feet of damaged cast iron pipe in my
house (built in 1900). My plan was to cut out the cast iron section
and replace it with PVC pipe, which would be coupled with the old
piping using a coupling band.

The problem is that the diameter of cast iron pipe is 2 1/2 inches,
which seems to be irregular nowadays as the closest pipe / coupling
band diameter I can find is either 2 inches or 3 inches. Does anyone
have any recommendations on what to do, or where I can find 2 1/2
piping / coupling bands?