My 1993 buick century will start and run great for about 15 to 20 miles,then it stalls out the engine will restart but stalls in gear.after 20 to 30 minutes it will run again and run fine for another 15 to 20 this car has only 93000 miles on the original engine and transmission

I have a feeling your fuel pump is on its way out...but start by changing your fuel filter first, should be under $20....ie..not enough fuel getting through..

There should be a purple wire with white tracer from ignition module to computer. That wire carries rpm signal to computer, w/o that signal, the computer won't ground the fuel injectors. With the engine cranking, you look for a dc pulse on that wire. If you have a digital multimeter that has a tach--duty cycle or dwell setting, it should react to a dc pulse.
My info on your model year, isn't that great.

This problem is commonly caused by a dirty automatic idle speed control valve and throttle valve. Buy a can of throttle valve cleaner (do not use carburetor spray cleaner!) from NAPA or Carquest (made by CRC chemicals) and spray it into the air intake while the engine is running, use up about 1/2 the can, engine will try to stall hold the speed up, shut it down and let it soak for 30 minutes, restart and blow out the remaining fluid, shut it down and disconnect the negative battery cable for 5 Min's to reset the base idle control

Injectors, even if one is bad, the increase in resistance in the SFI system kills the other injectors too. When it starts to run bad, unplug injectors one at a time to see if it runs better.

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.

i had the same problem with my 92 exept after mine stalled it wouldnt start for 20 - 30 mins... mine ended up needing a transmission flush for the stalling problem and i tried to drive everyday that helped
hope this helps in some way

check fuel pump pressure.it should be 41 to 47 psi.

Need to check for fault codes. Possibly a faulty sensor causing the fuel system to run rich or lean.

coil

you might want to chk. the crank sensor and or cam sensor. sounds more to me that it could be fuel problem. chk. fuel pressure. pump could be on its way out. don't be fooled by hearing the pump running as they sound like they are pumping but there not, at least not enought pressure to keep it running. pressure should be around 50 p.s.i.