Electron-phonon coupling in ZrCo2Sn is investigated within the density-functional theory and linear-response approach in the mixed-basis pseudopotential representation. Phonon-induced scattering is analyzed for excited electrons (holes) in two majority bands, which form the topological Weyl state. Although the electron-phonon coupling in the energy range under consideration demonstrates some dependence on the available phase space, the strength of the phonon-mediated scattering, λ, changes rather weakly with the hole (electron) energy and momentum, varying between 0.1 and 0.3. The momentum-averaged value of λ ranges from 0.25 to 0.45. The phonon-mediated scattering of electrons near the Weyl point is found to be weak enough to warrant well-defined quasiparticles. Most of the modes actively involved in electron scattering are middle- and high-frequency lattice vibrations, while the participation of low-energy acoustic phonons is significantly suppressed by electron-phonon matrix elements. Of the long-wavelength optical phonons, only the T2g Raman active modes generated by opposite vibrations of Co atoms make a noticeable contribution to the scattering of electrons.