  In this study, we present a novel family of Meixner-type $d$-orthogonal
polynomials, which are distinguished as a particular subset of multiple
orthogonal polynomials. We demonstrate their connection to the Lie algebra
$\mathfrak{su}(1,1)$ by identifying them as matrix elements of an appropriately
defined nonlinear operator. Utilizing Barut-Girardello coherent states, we
explicitly outline their key features, including recurrence relations,
generating functions, and $d$-orthogonality relations, among others.
