That's a twin of the original parent that had been disabled a long time ago. Well, the same API call worked! It now has a child called "API Test2". Tried again, with a different name and IP, and a 2nd child was added. I tried with my own credentials on a childless data source and it worked as well. Then I tried to add a child to a 4th data source, one that, like the original one, already had a child, and again got the "ERROR_CannotAddAgent (758)".
So I can add childs, but only if the DS is childless.