We have observed recently the Stark-tuned three-body Förster resonances 3×nP3/2(|M|)→nS1/2+(n+1)S1/2+nP3/2(|M∗|) at long-range interactions of a few cold Rb Rydberg atoms [D. B. Tretyakov, Phys. Rev. Lett. 119, 173402 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.173402]. The three-body resonance appears at a different dc electric field with respect to the ordinary two-body resonance 2×nP3/2(|M|)→nS1/2+(n+1)S1/2 and corresponds to a transition when the three interacting atoms change their states simultaneously (two atoms go to the S states, and the third atom remains in the P state but changes its moment projection), with the negligible contribution of the two-body resonance to the population transfer. It thus has a Borromean character and represents an effective three-body operator, which can be used to directly control the three-body interactions in quantum simulations and quantum gates implemented with Rydberg atoms. In this paper we theoretically investigate the coherence of such three-body resonances and we show that high-contrast Rabi-like population oscillations are possible for the localized Rydberg atoms in a certain spatial configuration. This paves the way to implementing three-qubit quantum gates and quantum simulations based on three-body Rydberg interactions.