  In this paper, we extend the notion of stochastic kinetic solutions
introduced in arXiv:2108.08858 to establish the well-posedness of stochastic
kinetic solutions of generalized Dean-Kawasaki equations with correlated noise
on bounded, $C^2$-domains with Dirichlet boundary conditions. The results apply
to a wide class of non-negative boundary data, which is based on certain a
priori estimates for the solutions, that encompasses all non-negative constant
functions including zero and all smooth functions bounded away from zero.
