I believe the timing has to be off just a little! Or the ignition box is going bad. the module on the fender.
A rich burn condition would cause too much fuel to build up and oxygen would be available at the catalytic converter during deceleration resulting in backfiring and excessive heat in the catalytic converter. Check the O2 sensor, air filter, injectors and plugs for anything that might allow raw fuel into the exhaust system.
Mapp sensor or you might need pugs and wires.
There are many reasons why your car might vibrate while it is idling. It could be running too hard for example.
Here is a link to a service bulletin that might help. http://www.fcsdchemicalsandlubricants.com/fad/tsb/031515.pdf Randy
If the car dies while idling, the timing might be off. Other causes can include a clogged fuel filter or a bad spark plug.
the timing is most likle out your timing belt jumped have fun check sparkplug wires to be in the right order
need to replace the intake manifold gasket
Sounds like the timing belt is going bad and the motor is out of time slightly. this motor is a dual overhead cam design and it is pretty tricky to change this unless you are a good mechanic.
It has been my experience that most backfiring problems are cause by intake vacuum leaks. You might want to check the torque on the intake manifold retaining bolts or it may be a worn intake manifold gasket. You might also want to inspect the vacuum hoses for cracks or loose connections. You might also check the timing. If the timing is off, it can also cause backfire and starting problems.
The backfiring is a sign of a lean condition. Perhaps there are some blockages in the various ports and passages in the carburetor.If it hasn't been done in awhile, you might want to get a carb kit and clean everything in some commercial carb cleaner, then blow it all out real good with compressed air, then reassemble with new gaskets, seals and floats.Also, make sure there are no vacuum leaks caused by bad gaskets or rotted tubing. Vacuum leaks can create a lean condition.
There are various reasons why your car would almost stall when idling. In most cases, this might be an indication of the engine lacking power or capacity due to the failure of the pistons. You should contact a mechanic to diagnose the problem.
Check you spark plugs. Probably going to need to replace them.