I don't think it can be done post-1900 (even without the Fifth Aliya, Israel would've come into existence on the same timeline as in OTL), but it can be done not far before 1900.
Basically, you want Zionism to be a politically weaker force. This means you want the anti-Semitic pressure in Western and Central Europe to be weaker. Arguably, you could get away with zapping the Dreyfuss Affair, which was a major influence on Herzl and on French Jews, so that means a POD in or just before 1894. Eastern European Jews would still look for ways to emigrate, but without the backing of Rothschild, Ruppin, et al, they would not mass-migrate to Palestine.
As a lower bound, if the Revolution of 1848 had succeeded in Germany and implemented a Greater Germany Solution, then most likely Germany would not have been so anti-Semitic in the late 19c, so German (inc. Austrian) Jews like Herzl and Ruppin would never have needed to be Zionist.