I would do it (in a mod, of course) by happening Zionism slowly come into the Jewish conscience starting in the 1850s, maybe as an Issue or something. Around the 1880s, you'd see migration to Palestine of Jewish pops from both liberral nations, and nations that aren't so great to the Jews. Ideally, some sort of pogrom system can be implemented for the less liberal nations, which will increase migration when triggered. Eventually, around the turn of the century, the World Zionist Congress will happen, and the Jews will start shopping around the Great Powers for someone to support them. If someone (not necessarily the owner of Palestine!) offers the region to them, there'll be a surge in immigration from the liberal nations for a couple years. If Palestine was offered by the owner of the region, this will taper off a bit, but stay pretty strong for a while. If Palestine was offered by a non-owner, Jews in that country will start agitating for a war of conquest. Either way, immigration by Jews will be matched by immigration by Arabs in Syria, Iraq, and Egypt.
A non-Palestine region could also be offered, though this would have to be an owned region, and the Congress is much less likely to go ahead, unless the pogroms are really bad. Something similar will occur, with similar native immigration where applicable.
Either way, the Jews (both there and abroad) will eventually agitate for independence, depending on how well they've been treated.