One connector is attached to the bottom of a container filled with liquid. When it is not connected it is closed and none of the liquid can flow out of it. However when it is in contact with another connector it then opens and allows the liquid to flow out of it. Any ideas where these kind of connectors can be found or made?
There are many, many different commercially-available designs of fluid connectors that shut off automatically when disconnected and open up when connected. They are available in plastic and metal, permanent and disposable, in all sorts of sizes. Try a search on "make-and-break fluid connectors".