Weren't the majority of Arab emigrants non-Muslims? Arab emigration seemed to mainly occur amongst non-Muslim Lebanese, and of course there's plenty of them in Latin America.
You'd also need a country small enough but also attractive enough to immigrants to make them the majority. Also perhaps some skilled efforts in the Ottoman Empire/Egypt to promote immigration to the Latin American nation of choice. The aforementioned Dominican Republic is a good example, and maybe also a Central American country or perhaps Ecuador. Anything else would mean Brazil and/or Argentina locking down on immigration and thus altering migration patterns. Also, make sure the US takes a hard line against Arab immigrants--the US already didn't like Lebanese immigrants much, so more anti-immigration legislation earlier. I know the 19th century US wasn't really anti-Muslim by the modern sense of the word, but maybe some early "Muslim panic" could get immigration from the Ottoman Empire shut off like immigration was from China or else severely restricted, also affecting migration patterns.
But all Arabs will still probably be disproportionately Christian of some church or another. I think a lot therefore wouldn't be Catholic. But Assyrians/Syriacs are not Arabs, even by language (a unique Aramaic dialect to go along with some of the Latin American Italian and German dialects?), and Copts really only count as Arabs because they all speak Arabic since the Middle Ages or so. Since to get increased Arab immigration you need emigration from Egypt too in addition to just Lebanon and to a lesser extent Ottoman Syria, well, it could be difficult depending on how you define "Arab".