I have done some research on this area and the American military forces in Koblenz during WW1 and especially between 1919-1923. This is very interesting and especially about the occupation with American forces in Koblenz.
General Wainwright was one of the Generals who was at Koblenz up until 1920. I reccomend you take a look at a couple of books. One has a definate bearing on what you are looking for and some history of what the father of your God-father and his mother went through maybe.
The first book is (1.) "Sleeping with the enemy; by Fred Strickert. It deals with the troops who were there and the fact that they did not build any barracks and were housed on or in the homes of the general population. You can imagine what kind of situation this causes with the Armed forces and the general population. It especially had an effect on the men of the town and the G.I's who were miles away from home and young as a rule. The book is on the internet.
It will give you a lot of insight and possibly answers some questions and pose some questions to you. It might give you some ideas in your search.
You have to keep in mind. That there was not a lot of troops there at the time. 1920 they numbered 15,000 and by 1923 it was down to a 1,000.
The next book (2.) "The Lorelei"-Fred Strickert".
A point in question. There was 2,122 soldiers who applied to get married over a period of time and about 1,213 were approved. 776 women did not want to get married and chose to take care of their own ( I might be wrong in my pharsing "their own"; but they chose not to marry.
There are mid-wives who left diaries who brought several of the children into the world. There are several people who have a common interest and you should try to get in touch with some of the relatives who are looking also. I will try and go back and get you an E-mail address. The town that was quite involved was "Mayen".
There was rules and regulations and guide lines set up and were inforced about GI's and the local women and there were supposedly punishments ; but later they dropped the restrictions and even provided transportation for those wanting to get maried; but they were imediately discharged from the service when they got home.
You are only dealing with the third Army. The next job is to find out what division, batallions or regiments were there at a given time. That can be obtained. I am sure. I will see what I can come up with.
At this point you have to ask yourself a question and don't get me wrong. The grandmother might not want the truth to be known. She might have been one of those who chose not to get married or might have deeper reasons. When you first see some one and it develops into a relationship or a quick romance. and the product of a child coming into this world and the indiavidual in her eyesight might not be worth it and she might just want it left alone and forgotten. The other side of the coin. Was it an american soldier or was it another person and someone she fell in love with and later it became a story about a G. I. and leaving it at that for the history of the family. Maybe to leave it to the winds and let it blow away and to remain forgotten. We can't judge them; because we didn't "Walk a mile in their shoes". It was just during and after a war. It put a lot of strain on peoples minds, hearts, and families. It had to be hell for some people. Especially when you are the product of what and who started the whole thing. Excuse me for getting long winded. Danny