Vanadium tetracyanoethylene (V[TCNE]$_text{x}$) is an organic-based ferrimagnet that exhibits robust magnetic ordering (T$_text{C}$ of over 600 K), high quality-factor (high-Q) microwave resonance (Q up to 3,500), and compatibility with a wide variety of substrates and encapsulation technologies. Here, we substantially expand the potential scope and impact of this emerging material by demonstrating the ability to produce engineered nanostructures with tailored magnetic anisotropy that serve as a platform for the exploration of cavity magnonics, revealing strongly coupled quantum confined standing wave modes that can be tuned into and out of resonance with an applied magnetic field. Specifically, time-domain micromagnetic simulations of these nanostructures faithfully reproduce the experimentally measured spectra, including the quasi-uniform mode and higher-order spin-wave (magnon) modes. Finally, when the two dominant magnon modes present in the spectra are brought into resonance by varying the orientation of the in-plane magnetic field, we observe anti-crossing behavior indicating strong coherent coupling between these two magnon modes at room temperature. These results position V[TCNE]$_text{x}$ as a leading candidate for the development of coherent magnonics, with potential applications ranging from microwave electronics to quantum information.
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