The alkaline earth metal trimer cluster dianions Be32- and Mg32- lie energetically above their respective monoanions and can therefore decay by electron autodetachment. Consequently, these dianions possess only short-lived resonance states, and here we study these states using regularized analytic continuation as well as complex absorbing potentials combined with a wide a variety of quantum chemistry methods including CCSD(T), SACCI, EOM-CCSD, CASPT2, and NEVPT2. For both Be32- and Mg32-, four low-energy resonance states corresponding to different occupation patterns of the two excess electrons in the two lowest p-σ and p-π orbitals are identified: Two states are dominated by doubly occupied configurations and can be characterized as showing σ and π aromatic character. The other two states correspond to the open-shell singlet/triplet pair. All dianion states are found to be highly unstable and to possess short lifetimes: They show resonance positions in the energy range 2.3-4.3 eV above the ground states of their respective monoanions and broad widths between 1 and 1.5 eV translating into femtosecond lifetimes. For both Be32- and Mg32-, the differences between the four states are small, but the triplet states tend to be slightly more stable than the three singlet states. Thus, in the case of the multicharged ion aromatic character of the excess electrons takes second stage while Coulomb repulsion takes front and center. In addition to the two isolated cluster dianions, model stabilization by small water clusters is explored. Our results show a dramatic drop in resonance position and width corresponding to a lifetime increase by 2 orders of magnitude. However, the "solvated" clusters are still resonances, and a more pronounced perturbation by, for example, yet larger water clusters or a ligand environment providing larger bond dipoles will be needed to fully stabilize two excess electrons localized on a small system such as an alkaline metal trimer.