Tennis is an official sport at the Olympic Games, originally from 1896 until 1924. Before it returned as an official sport in 1988, it was a demonstration sport twice.
There were two tennis tournaments played in Mexico in 1968. There was a demonstration tournament held in Guadalajara and an Exhibition tournament in Mexico City. I'm not sure what constitutes a demonstration and exhibition tournament. A men's and women's singles and doubles and mixed doubles events were held in both locations.
Tennis was also played at the Los Angeles 1984 Olympics as a demonstration sport - the first time professional athletes were officially allowed to compete in any Olympic sport. There was a men's and women's singles event, played at the Los Angeles Tennis Center at UCLA. Only players under 21 years old were eligible to enter the tournament. The winners were Stefan Edberg and Stefi Graf. Last time tennis was played as a demonstration sport in Mexico it was not a hit with fans, this time it was a sellout.
There was a demonstration of jeu de paume in 1924 (the sport was called real tennis at the time).