Of course we can help
Karl Winkler was the coach of Omonia Nicosia from 1958-1959, which is one of the most successful teams in Cyprus. Your source which calls it "FC Nikosia" is not exactly accurate as there are several teams from Nicosia, Omonia is just one of them. Others are for example APOEL and Olympiakos.
He is generally credited as a good manager for Omonia, who laid the foundations for the team to become a big footballing force in Cyprus. Omonia was founded in 1948, relatively late compared to most Cypriot teams. So Winkler was manager in the early years of the team, before the team had become a strong force capable of winning many titles. But in his time, he made the team stronger and more competitive than it had previously been. He made a positive impact on the club. Although he did not win any titles with Omonia, they won their first trophy 2 years after he left. So he is credited as having been part of this "transition" from small club to a big club.
I have no information that he became the coach of Cyprus. From 1958-1959 the coach was a Hungarian, Gyula Zsengeller. And from 1960-1967 it was Argyrios Gavalas. So I don't think Karl Winkler ever became coach of Cyprus.