It sounds like a simple cold start problem. Assuming all the routine maintenance is up to date. Timing and idle speed are at spec.
This should be fixable without too much expense. And it looks like you’ve ruled out the fuel pump and if you follow @Tester 's suggestion above and no fuel leaks out, the fuel pressure regulator as well, so that’s good.
Since you passed emissions with no issues, I doubt the problem is the MAP.
It could be the IAC, but since you say that part is fairly new, more likely if the IAC were the problem, it would be the control to the IAC, not the IAC itself. The IAC simply does the same thing you do when you press of the gas pedal, to increase the idle while the engine is cold. It is controlled by the coolant temp. On a 91 I’d guess though that the coolant flows right through the IAC to heat it up, and it works sort of like a mechanic thermostat, so there is no ECM or separate coolant sensor and vacuum line involved w/the IAC. (You should verify that by the repair manual specific for your car. Sometimes the IAC is called something else, like the “air valve”). Checking you coolant level is up to spec is worthwhile in any event. And checking that the engine coolant sensor is working is a good idea too. (Note: This is often not the same thing as what is used to measure the coolant temp shown on the dashboard guage, so your dashboard guage may show the coolant temp is normal, but the coolant temp sensor used by the engine could be on the fritz.)
My first guess though for the cause of your grief is the same as mentioned in one of the first posts above, the cold start injector. Either it isn’t working, or more likley, it isn’t getting the signal it is supposed to be getting during the Cranking phase. Look in your repair manual on how to check the cold start injector. (Newer cars don’t use cold start injectors, and yours may not have one either, so check your manual. In that case it would be a problem with the coolant temp sensor or the ECM not properly upping the fuel flow via the existing injectors during cranking).