As I have found to my cost on two of these cars, if you can't see where coolant is leaking from, then it is probably the pump.
I changed both pumps, one on a M104 E320 and one on a M103 300E, and it took me about 6 hours first time and 4 hours second time.
It is a PITA, needs loads of tools and lots of patience.
Make sure you get a new thermostat, it makes sense to change it at the same time.
Articles on this forum were invaluable in preparing for the job, I couldn't have done it without the folks on the forum.
Sorry to be the bearer of bad news.
1989 W124 300E
1991 R129 500SL