2001 buick century stalls wont restart till cools down for 1/2 hr

ignition module may be getting hot and cutting out..

You'll have to figure out if it is a fuel or ignition problem.
Is the check engine light on ?
could be several things including the fuel pump, pump relay, ignition module, or coil

You need to do a fault code test, to do that and see what codes are present follow the instructions at the link. Also check fuel pressure at the fuel rail test port. FAQ How to read older GM codes for free

Now that you've replaced nearly everything, the only thing left that I can think of is the oil pressure sending unit. If this is bad, the fuel pump shuts down, possibly causing the problem. However, before buying a new part, find the wire for the sender and ground it by attaching it to something on the engine. You won't indicate any oil pressure, but if this IS the problem, you'll know quickly. THEN go buy a new sending unit.

possible fuel pump relay.When engine stalls and wont restart listen at fuel tank for fuel pump to buzz for three seconds when key is turned on.

I don't know this car but if I was you I would start with the ignition system. First getting extra spark plug or tests light. When the car is running good, pull the coil or spark plug wire off and test for spark. By puting the sparkplug or tests light in the sparkplug lead. Then when the problem happens tested again to see if you have sparked. also pouring a little fuel down the intake system. If the car starts you have a fuel problem. If it does not start, you may have a bad ignition module are or coil. Good luck.

What you need to do is when it stalls out then check to see if your loosing fuel or spark.Check for spark at the spark plugs.don`t just check one.Check all the front 3 a least.If no spark then you probably have a bad ignition module.It is under the coils.Good luck.

possible ignition coil pack breaking down when hot....cools off and works again. pull plug wire off plug and check for spark when in this no start condition.vehicle must have air, fuel and spark to run.

fuel sending unit is faulty needs replaced unfortunatly you will be forced to buy the entire fuel pump (module). they are not cheap.