It's surprisingly easy to archive:

(scaleX and scaleY equals 2.5)
String[] values = {"Public", "Shared", "Private",....};
NumberPicker np=
(NumberPicker) findViewById(R.id.numberPicker);
np.setMaxValue(values.length-1);
np.setMinValue(0);
np.setDisplayedValues(values);
And simply set small layout_height and scaleX, scaleX:
<NumberPicker
android:id="@+id/numberPicker"
android:layout_width="wrap_content"
android:layout_height="50dp"
android:scaleX="2.5"
android:scaleY="2.5"/>
I do agree, that standard NumberPicker is hardly customizable, though.
I hope, it helps