If the paper is light in colour you could use a reflective opto sensor
such as this and put a black mark on the paper where you wanted it to stop. If the paper was dark in colour you could stick on a reflective marker wher wou want it to stop. An alternative would be to yse a slotted opto sensor and punch a hole at the edge of the paper where you want it to stop. You would arrange the output of the sensor to drive the motor when it was not at a marked point and stop the motor at the marked point. To restart the motor you would overide the sensor to start the motor. One it had moved away from the mark the button could be released. Posting some pictures and more information on the device may help members to come up with other suggestions
Les.