Wimbledon
The first sport broadcast on television during the 1936 Olympics was athletics (track and field). It's important to note that while these were the first Olympic events televised, they were not broadcast to homes. The viewing was limited to specially equipped theaters or viewing rooms.
The first live televised tennis tournament was the 1937 Wimbledon Championships in England. The BBC televised parts of the tournament, focusing mainly on Centre Court matches. This live broadcast is for general population, though only a few homes in UK had television sets in 1930s