The quickest - but cruellest - way to ensure a Muslim Lebanon is the 1860 Mt. Lebanon Civil War, where the French fail to make an intervention. This would have been difficult, given Napoleon III had gone to war with Russia specifically to gain the title "Defenders of Christians in the Holy Land". For all the guy's bumbling, he at least made an effort.
But here's the thing. Lebanon was at most 50% Christian. According to the constitution minted in 1948, a third of the people were Maronites, hence they had a third of the seats in Parliament. Demographics shifted, but the number of seats stayed the same. The Lebanese government hasn't done an official census since 1970 for this reason; the scramble for power along demographic lines might trigger a second civil war.
The Christians were a vast majority at the start - when it was just Mount Lebanon. In order to make the state viable, the French had to shave bits of the North from Syria to give it valid ports, and give them Beirut, which had an even split of Christians and Muslims. This had the effect of giving Lebanon a considerable (Sunni) Muslim minority, something the Lebanese Christian leadership feared would cause the Syrians to seek a casus belli - hence why they kept close ties to France and the West. The Shi'ites in the south were all dirt-farmers, but France didn't want to give the territory to Israel (something which upset many Zionists who wanted the territory up to the Leitani), so they wound up as part of Lebanon too; an underclass taken advantage of by the Christian leaders and the Sunni Opposition.