See their instructions here
http://www.surpluscenter.com/Instruct/I5-1647.pdf
On the starting relay - the motor appears to have a centrifugal switch (as most do) that connects L1 to the RED wire til the motor is up to speed - This lets the 120 volts energise the starting relay, pulling in the relay contacts (above the relay coil in the drawing) -
That puts both capacitors in parallel, increasing the total capacitance for starting.
When the motor comes up to speed, the centrifugal switch in the motor drops out, taking the START capacitor out of the circuit leaving the RUN capacitor.
They claim that motor draws nearly 10 amps, but uses only 440 watts - only way I see that happening is if the amperage is STARTING amps. Otherwise, 10 amps at 120 volts would be 1200 watts. (volts X amps)
Based on that, I think that a 10 amp, 120 volt AC relay would work - one I've used thousands of times (retired instrument/electrician) is the Potter/Brumfield KRP11-AN - it has TWO 10-amp sets of contacts, so if I were doing this I would wire BOTH sets of contacts in parallel. That way you would have some reserve capacity on the contacts, and they should last a LONG time.
BTW, if this motor REALLY only draws 440 watts, it would be rated at a maximum of 440/746, or .59 horsepower - still over half horse, and the slower speed should make your press act more like it had a 3/4 horse motor.
Still seeing no prob with this, as long as you have access to a way to (1) bore out your existing motor step pulley, and (2) fab a bracket that would bolt to the end plate of the new motor and match up to your existing motor mount plate (the one you move back and forth with the tension lever when you change speeds) - I'm thinking this would basically be a large "L" bracket, with a hole for the motor shaft, holes to match the motor end plate, and more holes in the other leg of the "L" to line up with the tension adjuster carriage.
Whew - as far as I can tell, I left out any more "brain farts" - HTH... Steve