Is there attic space above the wet ceiling? If so, get up there when it is raining and see if you can spot the drip. Will most likely be running down some structure before dripping, so the leak could be somewhere not directly over the wet ceiling. ID the location and call a roofer. It is much easier for them to fix if they can be told approximate location of the leak. Take some pics and show them when they come out.
Otherwise they will tell you they don't have a good way to isolate the leak location without knowing where it its and they will try to either sell you a new entire roof, or an entire side of a roof.
Usually when this happens it is a flashing issue. Your roof vent/s may have become partially dislodged and is allowing small amts of water in around them, or something similar like your plumbing vent, chimney, or anything else penetrating the roof. I would start with this. Walk to the street and then your back yard and see if any of the things that are normally on your roof are askew/missing, etc. I would even get up on the roof to physically check these things before calling a roofer. Could save yourself a lot of money, time coordinating them to come out/meeting them, and frustration.
If the flashing thing doesn't work, don't do the hose/quickcrete thing. Call a roofer. Often enough, the crap people do to try to solve things like this end up making the eventual fix much more expensive in the the roofer will have to address the dumbass fix and then address the leak, rather than just having to address the leak.
