I think the best way to preserve the rain water might be to seal it in full ziplock bags, without any air. That's how to preserve opened bottles of wine! Or, more precisely, one inflates a balloon in the wine bottle to block the air.

Unbuffered solutions such as rainwater will not keep a constant pH, which is why we buffer our solutions if we want a constant pH. But I think the rainwater pH will stay reasonably constant if you store it in a container without air. I'll recommend plastic - maybe a plastic storage box - because I think glass might be more likely to have reactive groups on its surface.

I'd think of a glass beaker? If that doesn't work I'm not sure what would. The thing is that water is pretty close to a universal solvent, so it will neutralize its pH on contact with most things given enough time. You may have to wait until it rains!