I was just doing some minor repair work to the wall, using some old paint I found - either leftovers from the original job, or colour-matched paint. Halfway through the tin started leaking. I have saved some of the paint in an old plastic yogurt tub with a lid that I think is airtight, as I don't want to have to try to get the colours matched. Will that do for long term storage, or do I need a metal tin? I also have some of those plastic containers with the clip-on lids that might be more airtight, and a few decking oil and lacquer tins.

As long as the air is kept out you should be fine.  Water bottles work well.