92 Saturn Doesn't Start Normally-Spark Plugs Carbon Fouled

I have a 92 Saturn SLI. It won't start normally. The engine doesn't turn over
when turning the key. If I hold down the gas pedal why turning the key I can
get it to a very hard start. I have to hold the gas down for a few seconds
and then rev the engine a little, black smoke comes out the back, but I can
get it going. However, when I stop the engine stalls. And I would have to go
through the same process to try to get it to run again.

I pulled the spark plugs and they looked carbon fouled. I replaced the spark
plugs and the car started normally and ran alright for about 20 miles and
then when I stopped at a red light it stalled out again and I had to go
through t the same rough start process again and keep fighting it at every
stop.

Is there a likely suspect for this situation? Someone suggested that the car
is running rich and it might be the fuel pressure. Does that sound likely?
What needs to be checked/replaced?