This solution is really really simple, has plenty of precedent in history, and yet I haven't heard it proposed seriously by anyone before. So here is goes:
Palestinians should convert to Judaism
According to Israeli laws, anybody who converts to Judaism can trivially get Isreali citizenship. Once sufficient number of Palestinians gets citizenship, not only will they no longer be persecuted as much (Israeli Arabs are still treated as second class citizen, but level of discrimination is much much less) - together with existing non-hawkish Israeli citizens they will constitute majority of voters who will ensure that Israel will become a country that's much more peaceful and friendly toward its neighbours. As a bonus on top of that such mass conversion would immensely piss off radicals on both sides.
Now you will very likely complain about freedom of religion and such stuff. But why are these people Muslim in the first place? Because their ancestors converted to religion of previous conquerors of these lands - some were forced to, others out of opportunism, perhaps some even out of genuine conviction - it doesn't matter. Is following religious choices of ancestors really worth all the death and suffering that exists in Palestine right now? I say no. Especially since the most painful part of such conversion - genital mutilation - they all underwent already.
This wouldn't be without precedent - not only religions like Islam and Christianity, but also languages like Latin, English, and Spanish, national identities, and cultures have all spread largely by members of the losing group adapting habits of members of the winning group. In fact it would be a lot more difficult to point to any major religion or nationality which didn't spread in such a way.
It's a topic for whole another post, but ignoring this is the primary reason why I hate most analysis of humans in terms of evolutionary biology so much - variance of human behaviour is almost entirely culture-driven, not gene-driven like they all pretend, and culture doesn't only spread from parents to children.
Anyway, it wouldn't be necessary for everyone to convert - as long as the portion of Palestinians who do is high enough - let's say half - it would completely alter current conflict dynamics enough to solve it. The die-hard few who care too much about Islam can then safety practice their faith in the emerging unified single state (with a huge Jewish majority, even if a lot of that would be rather unenthusiastic converts). As the law doesn't forbid it - children of Palestinian converts could choose whichever religion they wanted - Judaism, Islam, Catholicism, Baha'i, Spaghetti-Monsterism, or whatever. In practice vast majority would simply follow religion of their parents.
Everything else having been tried and having failed already - there is really only one alternative to such mass conversion - waiting a few decades for both Israel and Palestine (and if possible all other countries of the region) to undergo demographic transition from short lives and big families to long lives and small families. Countries after demographic transition are a lot less belligerent.
This is very much happening - but very slowly. According to CIA World Factbook total fertility (number of children per women) between 1990 and 2010 fell from 7.0 to 4.9 for Gaza Strip (still ridiculously high), from 5.0 to 3.12 for West Bank, and from 2.9 to 2.72 for Israel - moving them away from values typical for the worlds' war zones like Afghanistan's 5.50 and Democratic Republic of Congo's 6.11 and more like civilized world's 2.1 and less.
One day it will very likely happen - all will undergo demographic transition, and while they might still hate each other as much as they do now - they will express it like Japanese and Koreans - by flaming each other on the Internet - not in the good old way of bombs and bullets.
This will of course take many decades. My solution solves the whole problem overnight. Any takers?