I have a W201 190D, and it's transmission was replaced a few years ago. The replacement part has a 124 part number... (i.e. the replacement transmission must have been intended for some 300-series vehicle). This implies that the same transmission was used in the 190D-2.2 and at least one 300-series vehicle; whether or not the 300E and 190E 5-speeds are compatible is another question, but this at least shows that there was some compatibility in transmissions between the 124 and the 201.
Note that it's a 5-spd manual transmission in spite of the fact that the image linked below says "AUTO TRANS" in it.