Superfluid helium nanodroplets provide a versatile substrate to cool atoms and molecules, and to assemble weakly bound complexes. Absence of spin-relaxation mechanisms makes He nanodroplets ideal to isolate open-shell atoms and create a spin-polarized system. Here, we show the first coherent manipulation of such a system by resonant excitation of a magnetic-dipole transition. Observation of approximately 50 Rabi oscillations demonstrates coherent population transfer with minimal dephasing. Ours is also the first application of ESR spectroscopy to doped He nanodroplets. This unique environment results in extremely sharp lines and hyperfine-resolved spectra: those of single 39K and 85Rb dopant atoms presented here denote an increase of the Fermi contact interaction, which we can follow as a function of droplet size, reflecting the distortion of the valence-electron wave function due to the surrounding He.