As mentioned by Jared and Jorge in follow-up messages to your initial request there are quite a few of us Khouris (with different spellings as they mention...actually one of my brothers spells it differently--Khuri...)
However, I'm pretty sure that with some efforts on your part with older Khoury parents, family papers etc. you'll be able to quite quickly get to some lead to at least start an interesting search.
One good place to start (as many other things in Lebanon...) is with the religious background.There are Greek Orthodox, Greek Catholic, Roman Catholic, Maronite, Protestant, Syriac, etc. families with the Khoury name.
Another important thing is of course the place of origin that any of your relatives would remember (North South etc.) In my case, my family is from a village in the south of Lebanon, but I know that it was founded by a priest of a different family name who moved in the 1400's from a northern Lebanese village.