  We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a
two-dimensional mixture of A and B bosons, with attractive AB and equally
repulsive AA and BB interactions. In order to check universal aspects of the
problem, we choose two very different models: dipolar bosons in a bilayer
geometry and particles interacting via separable Gaussian potentials. We find
that all the considered clusters are bound and that their energies are
universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for
sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When
$a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction
changes from attractive to repulsive and the population-balanced AABB and
AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy
just below this threshold, we find an effective three-dimer repulsion which may
have important implications for the many-body problem, particularly for
observing liquid and supersolid states of dipolar dimers in the bilayer
geometry. The population-imbalanced ABB trimer, ABBB tetramer, and AABBB
pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model,
they break up at $a_{AB}\approx 2 a_{BB}$ where the atom-dimer interaction
switches to repulsion.
