Just looking at the dimensions of the motors the 1/8 HP motor in your first link looks the closest match. (I would have thought the motors would need to be more powerfull than this.) The shaft is very much shorter than the original motor so that could be a problem. (Depending on what workshop facilities you have.) Another factor you may need to consider is if the speed of the two motors is different at the same voltage it will probably change the aiming of the ball and cause it to spin. As the motor in the link is rated at 3000 RPM at 90 volts I suggest checking the speed of the original motor at 90 volts.
Les.
Les.