The cascaded Fluidyne pump
Designing a pump to run on renewable energy is difficult. Solar energy, doubly so. Assuming, on a moderately sunny afternoon, an insolation of 750 watt per square meter, about equal to one horsepower, and also knowing this energy is absorbed as heat and converted into motion at an assumed efficiency of 33%, which is more than any affordable solar panel can manage, an area of 15 square meters would be necessary to match the power output of a 5 HP pump engine. That's not very portable. For a portable system then, the inhabitants of Bihar, unfortunately, will have to make do with a much slower system than what's currently available to them, should they choose to use this system. Furthermore, doing this electrically would be prohibitively expensive, so a purely mechanical solution, preferably with as few moving parts as possible, is desireable.
A simple black surface in sunlight will not get hot enough to produce any meaningful amount of power using a stirling engine. Therefore a solar concentrator of some kind will be necessary. One of the problems with the sun though is that it has the annoying habit of not staying where it is in the sky, constantly shifting the focal point of parabolic mirrors or convex lenses. Fortunately, it does follow a straight path along the sky, so the best way to harness its power is to use a solar trough, which, once set up, oriented parallel to the Equator (an inexpensive compass could be mounted to the pump's chassis, possibly with Velcro to make it removeable, to make this process easier), will require no expensive solar tracking system, and no user intervention for the rest of the day.
Now, the most important aspect: now that we have the sun's heat, the solar trough nice and hot, how will we convert this heat into pumping action?
The main solution that springs to mind is the Fluidyne pump. This is, in essence, a Stirling engine with a liquid piston and a pair of check valves to pump water. Because there aren't many moving parts it's a very attractive system, but there's a problem: Stirling engines do not provide much torque because they often run at atmospheric pressure and with very low compression ratios. For the same reason a Fluidyne pump will not be able to pump liquid with much pressure head. There is a solution though, and the inspiration comes from electronics.
Instead of using the pair of check valves, the hydraulic equivalent of a Villard cascade seems like the solution. This cascade, in electronics, is used as a voltage multiplier, converting alternating current to direct current at any voltage you like. In very much the same way it is possible to build a Villard cascade using not much more than some hoses, some check valves and some Y-connectors. This cascade can then be lowered into a well of any depth you like.
And there you have it: a solar-powered pump. It's reasonably reliable, the only moving parts being some check valves, reasonably easy to repair if it ever does go wrong, and, most importantly, cheap and easy to make as well. The material cost to build a pump like this is probably no more than 200 dollars.
As for the disadvantages: pumping speed will not be that high, much like a Villard cascade can't deliver that much current. Its current is limited by the frequency, and the size of the capacitors. Similarly the pumping speed of this system is limited by the amount of water that can be stored in each segment of the cascade, determined by the hose's diameter and each segment's length, of course. And the latter is, unfortunately, limited by the pressure head achievable by that Fluidyne, which isn't that great. Also, in normal operation, the cascade has a certain amount of dead volume, filled with air, which is compressible, and so will dampen the alternating pressure output of that Fluidyne. This effect can be mitigated by sizing the engine to be big enough. Taking the air pressure supply from the hot side cylinder would be better still, but the hoses weren't meant to be heat-resistant, so that's not an option.
But it will work, and it is cheap. And because the cascade has an inherent speed limit, it makes no sense to make the solar concentrator that big, and because of this, it can be portable. Also, because of its low price there's plenty of budget left to add in a drip irrigation system to lower the water requirement, and though about half a liter per second would be a reasonable estimate for this pump, which should be enough, even a few extra pumps could be added, should the situation require them. It's exactly what Bihar, and indeed every dried-out society on this good Earth needs. All we need to do is build it.