1991 Buick Regal Engine stall on acceleration

First thing to check is fuel pressure with mechanical gauge, should be at least 40psi and hold that pressure with pump off. If pressure will not hold after pump is off, then fuel pressure regulator diaphram is ruptured and would need to be replaced.

If OK, then have mechanic hook up ECM to scanner and look at MAP/MAF output and TPS output.
If either sensor is showing abnormal readings, it will cause engine to stall.

Although this is OBDI ECM, most shops should be able to read live data, mechanic can read all sensor output and look for sensors out of range or showing static readings.

If fuel pressure holds at 35psi, "blip" throttle with gauge attached, pressure should rise quickly 4-5 psi. If pressure stays the same or goes down, remove vacuum line to FPR, look for gas, if present then FPR is bad.

Also you will need to get live scan data to look at sensors as mentioned previously.
Mechanic could also look at ignition advance, ignition advance should go up as rpm increases.

Post results and any additional information you have, for example, high idle speed, coolant leaks, last tune up etc. So we can solve the problem.

I will call additional resources from other techs, if needed, until we can isolate the problem.