One of the most basic ways is to drag a wheel across the ball surface with a scale attached to measure the force.
You would have to be creative for fixturing. I would use 3 wheels (or whatever object you want to measure) to get 3 even points of contact. Fixture them to hold them steady, and add weight to get an even number to calculate so the total (including the wheels) is 10 or 15 pounds.
Take the fixture of wheels, remove the fabric from the ball and place it on a table. Make sure the fabric is held secure. Connect the scale to the fixture of wheels and drag. The number read, before the fixture of wheels skids, is the static force. The number read while the wheels skid is the kinetic force. Take the readings and divide them by the 10 or 15 pounds (whatever the fixture weighs with the wheels), and that is your coefficient of friction. The higher the coefficient of friction, the more grip there is.
I am sure if I missed something, it will get corrected for you.
Hope that helps!