While dealing with a Hamiltonian with a continuous spectrum, we use a tridiagonal method involving orthogonal polynomials to construct a set of coherent states obeying a Glauber-type condition. We perform a Bayesian decomposition of the weight function of the orthogonality measure to show that the obtained coherent states can be recast in the Gazeau-Klauder approach. The Hamiltonian of the l-wave free particle is treated as an example to illustrate the method. Published under an exclusive license by AIP Publishing.