Is there an efficient construction for a trilinear pairing that has been used in theory or practice
This question has been open for long now, and after some research I think I have the following answer

There has been two candidate schemes proposed for multilinear pairing by Garg, Gentry,  Halevi and Coron, Lepoint, Tibouchi.

However either do not have a security proof and their security is given by extensive cryptanalysis. 

So, to sum it up, although it is possible to implement a "trilinear" map, these maps are NOT (provably) cryptographically secure.