The Collaborative International Dictionary of English v.0.48:

Tivoli \Tiv"o*li\, n. [Prob. fr. Tivoli in Italy, a pleasure
   resort not far from Rome.]
   A game resembling bagatelle, played on a special oblong board
   or table (

   Tivoli board or Tivoli table), which has a curved upper
      end, a set of numbered compartments at the lower end, side
      alleys, and the surface studded with pins and sometimes
      furnished with numbered depressions or cups.
      [Webster 1913 Suppl.]