Tivolians were the inhabitants of the planet Tivoli.
History
Tivolians were one of the oldest species in the galaxy. Their home world was conquered multiple times.
Culture
At first glance the Tivolians were a society of cowards. They never defended themselves and did everything they could to make their conquerors as comfortable as possible. The Eleventh Doctor considered this to be an aggressive form of cowardice. The Tivolians didn't fight; they survived by outliving their conquerors. (TV: The God Complex)
Behind the scenes
Although this demonym was never quite used on screen, it's a logical extrapolation from the word Tivoli.