What we would need for a good POD is Israeli cooperation with the United States over its space program, or at least some desire to compete with the USA and the USSR. Israel had choosen to purchase the Jericho from France, but it would be better that Israel in the late 1960's purchased a form of the Titan, later renaming it the Shavit. Any equipment that is developed for such a program would likely be reminiscent of the American space program (it is likely that they would receive aid in such an endeavour from the United States), and the program would begin by the middle of the 70's.
The roadlock then becomes funding. Today, the Israeli budget is a million dollars for its space program, and GDP is around two hundred billion. Combined with the cost of their military, they would not be able to pay for as ambitious a program as Apollo, which in today's currency cost one hundred seventy billion dollars. Therefore, the program must be drawn out over a decades, similar to how the Chinese are doing it now (though they clearly could be doing MUCH more if they properly funded their program).
So we have the first one-man and two-man missions in the 1970's, and then three-man missions throughout the first half of the 1980's; the latter is mainly to test equipment for the planned lunar landings. Sometime between 1987-1989, the first lunar landing takes place, and the Star of David is planted upon the moon. However, whether they would be second is up to debate. If they seriously decided to make an attempt, the Soviet Union might try and beat them to the moon, and likely would (they already had developed much of the equipment in the past decade, and it would only need to be modernized).
Some other interesting developments would probably be a serious effort by Iraq and other Arab nations to develop a space program (and possibly plant the crescent moon upon its surface) and an early begining to the Chinese Space Program (which had failed to jump off in the 1970's and again in the 1980's).