Polynomial algorithm for correlated equilibrium
The linear program for computing a correlated equilibrium in a game has size that is polynomial in the size of the game matrix: i.e. exponential in the number of players. The scheduling game that you describe is an $n$ player game, so the linear program will not be polynomially sized. However, it is a compactly represented game, so you can in principle use the Ellipsoid approach of Papadimitirou and Roughgarden.

If you are ok with an approximate correlated equilibrium, there are much simpler and easier to implement approaches based on no-regret algorithms. For a textbook exposition, check out Chapter 4 of Algorithmic Game Theory.