Abstract: ollinear magnets in honeycomb lattices under the action of time-dependent strains are investigated. Given the limits of high-frequency periodically varying deformations, we derive an effective Floquet theory for spin systems that results in the emergence of a spin chirality. We find that the coupling between magnons and spin chirality depends on the details of the strain such as the spatial dependence and applied direction. Magnonic fluctuations about the ferromagnetic state are determined, and it is found that spatially homogeneous strains drive the magnon system into topologically protected phases. In particular, we show that certain uniform strain fields play the role of an out-of-plane nearest-neighbor Dzyaloshinskii-Moriya interaction. Furthermore, we explore the application of nonuniform strains, which lead to a confinement of magnon states that for uniaxial strains propagates along the direction that preserves translational symmetry. Our work demonstrates a direct way in which to manipulate the magnon spectrum based on time-dependent strain engineering that is relevant for exploring topological transitions in quantum magnonics.