In this paper, the authors describe explicitly all four-dimensional self-dual Einstein metrics which admit two linearly independent commuting Killing vector fields. For scalar-flat metrics, such a description (in terms of a harmonic function on \(\mathbb{R}^3\)) was already known. Here, for metrics with non-zero scalar curvature, a classification is given in terms of a local eigenfunction of the Laplacian on the hyperbolic plane (with the eigenvalue \(3/4\)). The proof relates this result to work by others in the field (Joyce, Tod, Ward). Further, the authors describe the self-dual Einstein metrics which arise as quaternion Kähler quotients of the quaternionic projective space \(HP^{m-1}\) by an \((m-2)\)-dimensional family of commuting Killing vector fields. A similar construction yields non-compact but complete self-dual Einstein metrics of negative scalar curvature.