The obvious militia are the Lebanese Christians. They far outnumber the Shiites, and if given the weapons and training would be a better army for Lebanon than the regular army.
There are several good reasons that the US could arm and train them, and their natural contention would not be against Israel, but against the Hezbollah and Syria.
Sounds like a good idea to me ... but if the media ever suspected that the U.S. was supporting them, they'd raise hell. Remember their fury about Reagan's support of the Contras in Nicaragua, and having the stupid Iranians provide the funding?