  We study graded rings of meromorphic Hermitian modular forms of degree two
whose poles are supported on an arrangement of Heegner divisors. For the group
$\mathrm{SU}_{2,2}(\mathcal{O}_K)$ where $K$ is the imaginary-quadratic number
field of discriminant $-d$, $d \in \{4, 7, 8, 11, 15, 19, 20, 24\}$ we obtain a
polynomial algebra without relations. In particular the Looijenga
compactifications of the arrangement complements are weighted projective
spaces.
