The Israeli populace is well trained and with some military experience; if there is to be a military coup there, it would be very popular or it would not outlast the legitimate government's cry for help. If popular, why not just elect the government they want?
I think this whole thread on the other hand is not paying enough attention to the context of superpower clientism, especially in the Cold War context. The thread's contributors are all assuming every coup is the result of purely internal politics when we should all realize that a great many of them are engineered, or at least encouraged, by great power interests far removed from domestic politics, and that if we wanted to explain the survival of many governments (these types being more often than not imposed by an initial coup) without reference to their Great Power patrons, we'd be pretty much at a loss to do so. Client governments need not, in extreme cases, rely on popular support at all--their economies and general technical development need not be capable of paying for or maintaining high tech and otherwise expensive paramilitary kit, not if some Uncle Sugar somewhere else in the world finds it on the whole worthwhile to kindly donate the tools of oppression. In that case, the primary basis of power in such regimes does not lie in their country at all, but in the favor of powers far overseas. I think if we weeded out all such cases as irrelevant to the theory and practice of stable civil government, we'd have a lot fewer coups to account for...but we'd also have a much reduced statistical universe of genuinely national states to consider too!
Anyway the question here is, why not India and Israel? The cases are quite different from each other, but I think in addition to valid points such as India's deliberately designed checks and balances and Israel's universal conscription, we have the fact that to put it bluntly neither of them is in the category of a typical Third World nation.
India is of course in most respects a classic case of what Third World means--but its sheer size, and the depth of its democratic traditions despite aberrations protect it from being capable of domination by some colonel funded by a black CIA budget. Had India's founders not taken care to develop an elaborated system designed to achieve checks on their military, it might have been possible for either American or Soviet agencies to subvert its armed forces somehow and impose a compliant dictatorship, but vice versa I think a small country that was decolonized with similar prudent political measures could still have been overturned anyway. Maybe size is not the key; in Central America there is the example of Costa Rica, a country which has not, since the 1930s anyway, been subject to dictatorship, avoiding being steamrollered by the Yankee machine. To be sure I believe this has been largely the work of a leadership that recognized that Uncle Sammy was going to get its way one way or another and resolved to trim the political sails to minimize any perception of threat and to make Costa Rica available to US interests, such as bases for the Contras raised against the Sandinistas in Nicaragua in the 1980s. But the nation has, perhaps at a high price, kept its effective independence and maintained civil liberties. (For one thing, it doesn't have an Army to pull a coup with, military forces having been much curtailed there).
But I do think given the challenges Indian nonalignment have posed to exasperate Western interests with over the scores of decades of Indian independence, a big part of Indian independence continuing meaningfully is its sheer size making a coup in foreign interests that much more difficult to carry out.
Israel on the other hand has got a status with respect to the developed European nations and the USA especially that makes support of this state despite the trouble it brings with the majority of people in the region attractive. The siege mentality of the dominant group of the nation, combined with ready support coming to them pretty much unconditionally, and the universal conscript service of all Israeli citizens, again makes a coup by a small foreign backed clique unlikely and certain to be fought vigorously should anyone foolishly attempt it.
I believe that if we somehow had a situation where the great powers were checked somehow from gross interference in the sovereign affairs of smaller nations, we'd see a lot fewer coups across the board.