  Electrons may form inter-site pairs (dimers) by a number of mechanisms. For
example, long-range (Fr\"ohlich) electron-phonon interactions and strong
on-site Hubbard U allow formation of small light bipolarons in some lattices.
We identify circumstances under which triplet dimers are strictly localised by
interference in certain one- and two-dimensional lattices. We assume a U-V
Hamiltonian with nearest- and next-nearest-neighbour hopping integrals t and
t', large positive U and attractive nearest- and next-nearest-neighbour
interactions V and V'. In the square ladder and some two-dimensional bilayers,
if the dimer Hilbert space is restricted to nearest- and next-nearest-neighbour
dimers, triplet dimers become strictly localised for certain values of these
parameters. For example, in a square ladder with t' = t and V' = V, all triplet
bands become flat due to exact cancellation of hopping paths. We identify the
localised eigenstates for all flat bands in each lattice. We show that many of
the flat bands persist for arbitrary t/ t' so long as other restrictions still
apply.
