You need limit switches, i.e. "turn until button X is pressed, turn until button Y is pressed". A lever microswitch would be the appropriate type of switch.
Without some sort of feedback mechanism there's no way to reliably make a continuous rotation servo turn a set distance.
As an alternative, you can find a few servos that will allow a repeatable number of rotations. They are referred to as "winch servos" and usually go anywhere from 1 full turn to 4 full turns. They operate just like regular servos ... with the exception of the greater range of rotation.