Why would tapping on a Cavalier coil assembly make it run fine when otherwise it stutters and misses and does not want to start or run correctly?

Replace the coil pack. You can buy this part at any auto part store and have a nechanic put it in for you or do it yourself if yer feelin froggy but you need a new coil assembly or new wiring and connection to it. you can also probably find a good coil assembly from a junkyard as these usually outlast the cars the reason it works when you tap on it is the coils are burining out from the inside and losing their connection. When you tap on it you cause the vibration to make the coils hit a "hot spot" as electricians call it. anyway replace the coil assembly.