Water weighs 62.3 lbs/cu .ft. The parlor car probably weighs 1200 lbs. 1200/62 = about 20 cu .ft. We need to have about 20 cu .ft. of air pushed under water to keep the parlor car above water. 15 cu.ft will keep 900 lbs above water. Crew weighs about 700 to 800 lbs. Car weighs about 300 to 400. Exercise Balls are 30" diameter. V = 4/3pi R^3 = 8 cu .ft. What?
I'll try that again with The Sphere Calculator

radius = 1.25 ft
Volume = 8.18123 ft3
Surface Area = 19.63495 ft2
Circumference = 7.85398 ft

It will take 500 lbs to push the ball under water. It would take 3000 lbs to push 6 balls under water so 1200 lbs would only push them down 40%. That should be about right.

I bought 85 cm Spheres for $35. J-Fit Pro series in Silver. Pro series is stronger and 85 cm is 33" dia. and 35% more volume than 75 cm. And to support entire car with people only 30% draft.

   85 cm ball details 33" dia. 10.9 cu.ft 678 lbs to submerge. 6 balls support over 4000 lbs. 1200/4000 = 30% draft. That's only 200 lbs/ball. To lift the car completely out of the water, there is less weight on the spheres than when I sit on them. I am going on a diet.

   PROPELLER INFO: Propellers have two numbers. A Propeller used for pedal boats might be 12 x 16. The first number is the diameter. The second number is the pitch. Pitch is defined as "the distance a propeller would move in one revolution if it were moving through a soft solid, like a screw through wood." For example, a 21-pitch propeller would move forward 21 inches in one revolution. From Understanding Propeller Pitch.

   I measured the angle of the blade on a table by eyeball. It looks to be 73 deg. So if that line is continued out for the length of the circumference, then the pitch is the length along the table edge. The blade is about 23 1/2" dia. which is 72" circumference. Cos(73) x 72 = 21" So the prop (or screw as they call them on the high seas) is 24 x 21 roughly. With no slippage at 300 RPM, the Car will go 21 x 300 x 60 / 12 / 5280 = 6 MPH. So it may go 2 or 3 MPH in real life. I think Kimric's prop is as close to perfect as we could guess, for a four person, 1200 lb pedal car floating on helium filled exercise balls.

   HELIUM FILLED SPHERES: Donald Day wants to help us fill the exercise balloons with Helium. He has calculated that they will float in air. This deserves another drawing, which I will make soon. But I think we should give this a shot.

   4/28/11 Update: 85cm Spheres (exercise balls) have about 11 cubic ft. Helium lifts 1 oz/cubic ft. (1 gram/liter) = about 3/4 lb. Not much. So 85cm = 33" diameter spheres weigh 5.0 lbs. with Air in them. With Helium, they would weigh 4.25 lbs. So the Helium idea won't float.
   Let's figure out how big the spheres would have to be to just float in air. Surface area is 4pr2. So 33" diameter is 3420 sq. in. = 23.75 sq. ft. and the vinyl weighs 5 lbs. = .21 lbs/sq. ft.   

(r in inches) (4/3)*pi*r3*.063 / 1728 = 4*pi*r2*(.21)/144
r = .21x3x1728 / 144x.063
r = 120" exactly
20 foot balloon = 264 lbs of vinyl = 264 lbs of lift.
That's kind of surprising. I would have guessed half that.

   Shannon has built two Styrofoam pontoons. They are about 18" x 13" x 48" and have curved ends. They have about 5.5 cu. ft. and weigh about 30 lbs. So They will support about 300 lbs if submerged. If the car weighs 1200 lbs, with these it will weigh 1400 lbs which means we need 5 of these minimum. I figure the total weight of the pontoons to be 200 because of the supports needed to fasten them. They are too big to carry on the Parlor Car. Not sure what his objection were to the 5 lb, 11 cubic foot deflectable spheres. Probably the supports for the spheres would have been too big to carry as well.