This paper addresses the challenge of asymptotically rejecting sinusoidal disturbances with unknown time-varying frequency and bounded variation rate. We introduce a novel, data-driven approach for designing Linear Parameter-Varying (LPV) controllers, utilising only frequency domain data from a Linear Time-Invariant (LTI) Multi-Input Multi-Output (MIMO) system, thereby eliminating the need for a parametric model. Our method involves a two-step iterative algorithm that solves convex optimisation problems in the frequency domain. Closed-loop stability is guaranteed through Integral Quadratic Constraints (IQC), which characterise the bounded rate variation of the LPV controller’s scheduling parameters. The approach is experimentally validated by designing a controller for the hybrid microvibration damping (MIVIDA) platform, developed for spaceborne applications.