Sometimes an apparently well-formed question can suffer from a "category error", such as in "Is the present King of France bald?" or "What noise would the programming language Pascal make if you dropped it on the floor?" In such cases, an appropriate way to "answer" the question is to point out the category error, instead of just saying, for example in the previous examples, "No" and "'CLANG!' (although some authorities argue "SPLAT!" is more accurate)". This Buddhism question isn't completely prone to this problem, but one aspect of it might be. So I'm going to attempt that kind of answer.
First, I'm with the Dalai Lama in that if science proves something in Buddhism to be wrong, then Buddhism would have to adjust. However, it's important to understand that there are certain kinds of true things that science simply cannot prove wrong. That's not because, as with many things in the past, our science just isn't advanced enough yet. It's because the scope of science doesn't cover everything important we might want to say. This goes against the modern prevailing view, sometimes called, often by its detractors, "scientism", which is really a modern version of positivism. However, it is not difficult to see that such scientism isn't obviously true.++
As an example, take the law of gravity, and in particular the component that says that "the gravitational force between two masses varies inversely with the square of the distance between them". That is very deeply established in science, and has been for centuries. If it were proved wrong, it would shake things up a lot. But science could indeed prove it wrong. In fact, there is already some evidence, surprising though it is, that in certain situations, the inverse square law isn't exact.
But now take the proposition "2+2=4". Philosophers would refer to that as a "necessary" truth. Science cannot ever prove that statement wrong because science relies on that statement and, more to the point, science does not deal with such truths. They are important truths that lie outside of science (in fact the existence of such statements doesn't break positivism which is broader than scientism, but it does constitute something that science cannot disprove).
Another one: "people typically experience redness when looking at tomatoes". Now science could certainly show that the frequency of light reflected off tomatoes corresponds not with red light but with blue light, but that doesn't change the fact that we experience redness. Science would probably come up with a theory as to why we experience redness when exposed to blue light (for example, perhaps we'd discover that tomatoes emit a certain gas that confuses our brain's color recognition system, leading us to experience redness instead of blueness), but as I say that would explain why, it would not disprove that we experience redness.
So, what about something like "there is no rebirth". Well to me that is clearly a statement that lies outside the scope of science, certainly of science as we usually use the word. To be a "scientific" statement typically means in practice that we can construct some kind of experiment capable of allowing us to make observations confirming the statement's truth and, even more important, observations confirming the statement's falsehood. But scientific observations are observations of the natural world and it's not clear that "rebirth" is posited as a phenomenon within the natural world. Now it's possible to argue, or at least to claim, that there is nothing but the natural world, but that's just begging the whole question. A claim that "natural science is all there is" is itself not a statement of natural science, so where does that leave it?
This doesn't mean, of course, that there's nothing in Buddhism that science couldn't disprove, but it does exclude a whole bunch of things from being disproven in that way. For example, I'd say that the entirety of the Four Noble Truths lies outside the scope of science. I'm not saying that they are necessarily true, nor that they couldn't be shown to be false. But science cannot do that, any more than gardening or cookery can.
++ Note that I'm not saying that scientism argues that science can know everything. Even the scientistic view allows that some things may simply never be known. I'm making the point that scientism typically argues that if something is knowable, science will eventually, in principle, figure it out; and that if science cannot eventually, in principle, figure something out, then nothing else will.