Generation of muon beams with protons on a current-carrying target followed by a lithium lens and a quadrupole decay channel is considered. A 8 GeV proton beam from the Fermilab Booster is used to provide a muon beam for the MUCOOL experiment for ionization cooling demonstration. The proposed scheme can also be used to create muon beams with a fraction of a 1 GeV proton beam of the Spallation Neutron Source. Monte Carlo simulations of the entire system are performed. For both cases optimization of the target and matching lithium lens is done. It is shown that such a set followed by an inexpensive decay channel based on quadrupole magnets with and without RF cavities provides a rather intense bunched muon beam.