The electron-phonon interaction in electron-doped single-layer MoS2 is investigated using first-principles calculations. The electron-phonon coupling is found to be very weak at low doping levels. It then grows rapidly to a maximum of lambda approximate to 1.7, after which it begins to decrease with additional doping. The superconducting transition temperature is expected to follow the same trends. This behavior is attributed to the growth and shrinkage of Fermi sheets with different orbital character. These results, which are similar to the experimentally observed superconducting dome in gate-tuned MoS2 thin flakes, reveal that having the right combination of electronic states at the Fermi level is crucial for optimizing the electron-phonon interaction in this material. By appropriately tuning the band structure, it may be possible to further enhance the superconducting properties of this material.