Howdy Chris:
An easy way is to get some modeling clay, press it into the dish of the piston and level the top with some sort of straight edge.
Now peal the clay out of the dish and drop the clay into a pre filled graduated becker. If the beaker is a 50 cc syringe, fill it about half full. once you've dropped in the clay note the before/after difference. That will be the volume of the dish. It is not necessary to maintain the shape of the clay once it is pulled from the piston dish. The volume displaced will not change with the shape.
The taller and narrower the becker the more accurate you will be able to be. I prefer a 50 cc dispossable Ag type syringe to a 1,000cc becker. I prefer to use auto trans fluid as my liquid mediam because of it's color. It is easier to see and has less surface tension then water. It is messier.
Adios, David