Plenty of ways. Of course, it's harder if you want the present nations with the borders defined at the San Remo conference, because it almost automatically kills whatever hope may have existed to have a Hashimite Greater Syria or something similar and, therefore, the framework in which the Faisal-Weissman accords had a chance (not that they had much of one, but that's a possibility).
The British fairly consistently mishandled the situation in the Interwar, incidentally managing to alienate both the Arab and Jewish leaderships. Had they avoided to support the rise of Hajj Amin al-Husayni to any prominence (apparently he lacked religious credentials and his choice as Mufti was political, with colonial support) for example, that would have contributed a lot. Even with a better British management, the situation is likely to grow tenser through the Twenties and Thirties, but you have better chances that cooler heads may prevail on either side (or develop more balanced views toward the Other). The best endgame in this situation is likely a single binational state with something akin to Dominion status (probably not actually a formal Dominion however) whose national identity might conceivably cemented in the participation to WWII. Lots of luck required, and I don't think that putting al-Husayni out of the equation would be anywhere near enough.
However, you'll need the British have the rare foresight to realize that it was imperative to build trust between the parties (the lack of which has been arguably the single most important factor in the ongoing and increasing intractable nature of the conflict) and help them reaching a stable political settlement.
There were plenty of occasions post-war for at least limited detente, which turned out to nothing. One notices a worsening pattern of hardliners on both sides getting a larger say in dictating the line.
But arguably, there were times when the pattern could be broken.
For example. have Nasir somehow manage to obtain the Suez Canal kinda amicably, without the 1956 war. Israel is not as widely perceived as the Imperialism's agent in the region, and the Egyptian regime has less reason see it as the quintessential enemy (this might improve the lot of Egypt considerably). The is probably no occupation, no recognizable Six Days War, no settlements whatsoever. Jordan, essentially a Palestinian state in this scenario, probably has some ugly moments ITTL, but in the end a final settlement with Israel with a mutually acceptable border is agreed upon and, if the Israelis feel less pressured and paranoid, may accept to some sort of compensation scheme for refugees, who, however, cease to be refugees and have Jordan to go. Someone would have to throw some money at it, the US might. Of course, I am extrapolating a best case scenario here. Plenty of ways for everthing to go wrong at any turn with comparable premises.