According to this answer it's possible to count how many non isomorphic triangulations correspond to a particular polygon.
I've also found here that there's the possibility to generate a tree containing every non isomorphic triangulation. So each node is associated with a triangulation. The goal is to access to a particular triangulation without generating the whole tree. Please note that I don't need to specify the particular structure of the triangulation: if the tree has 42 node and i want to access to 28th node I'd like to access to the node associate uniquely to it.
Anyway it's just one of the possible approach, all i need is an enumeration or a mechanism of uniformly at random choice of one of the triangulation.