  The concept of free fermion topology has been generalized to $d$-dimensional
phases that exhibit $(d-n)$-dimensional boundary modes, such as
zero-dimensional (0D) corner excitations. Motivated by recent extensions of
these ideas to magnetic systems, we consider 2D quantum paramagnets formed by
interacting spin dimers with dispersive triplet excitations. We propose two
examples of such dimer models, where the spin-gapped bosonic triplon
excitations are shown to host bands with nontrivial higher-order topology. We
demonstrate this using real-space Bogoliubov--de Gennes calculations that
reveal the existence of mid-bandgap corner triplon modes as a signature of
higher-order bulk topology. We provide an understanding of the higher-order
topology in these systems via a computation of bulk topological invariants as
well as the construction of edge theories, and study their phase transitions as
we tune parameters in the model Hamiltonians. We also discuss possible
experimental approaches for detecting the emergent corner triplon modes.
