In order to help you answer your question, it is important to define what you consider to be the modern era. In my response, I am focusing on the time period from the twenty-first century onwards, as this is what is usually considered the modern era.
You could use the Olympic Games of 1936 in Berlin as an example of how sport was used as a tool for social control. Hitler's propaganda machine successfully managed to turn this event into a way of presenting the Nazis' idea of the perfect, Aryan human. Through broadcasting pictures and footage of blond, muscular athletes, the Nazi Party was able to continue to control what society thought, as it helped to underline and encourage what the party wanted the German people to believe. As this helped to reinforce their anti-Semitic views, you could definitely use this as an example of how sport was used as a tool for social control.
Another example of how sport could be used as a tool for social control is sport during the German Democratic Republic. In communist Eastern Germany, sports were very popular and many young people were actively encouraged to participate in sports. However, in order to be allowed to participate and to receive coaching and training, it was a requirement that the person and their family were considered true followers and supporters of the East German government.
Therefore, by tempting young people with athletic success, the East German government was able to control young people as well as their families, as it was a way of making sure that everyone stayed in line. Speaking out against the regime would have immediately resulted in the end of a person's sporting career, so sport was used as a very effective tool for social control in those days, too.