I have a '59 Dodge Coronet with a transplanted '77 400. It has a Holley 4bbl... 600-650, I'm not sure. I don't have the carb# at the moment.

Whether I take off hard or slowly the carb hesitates, stubbles and "sneezes".... I say sneezes because it really doesn't do the usual backfire. It sounds pretty much like a sneeze.

I have adjusted the air mix, ignition timing, tried to make sure there are no vacuum leaks.
It had a 31 squirter that I replaced with a 37 but that doesn't seem to matter in the least.

Any suggestions?

there was a good post on the causes of a "sneeze" vs a "backfire" but I dont remember what the content was. At least here's a BTT for ya.

That sounds lean to me (unless it's SO rich in which case you'd see black smoke when you step on it). If you just ease into the throttle and it still stumbles, probably not squirters.

What jets are in the carb? Fuel level in the bowls set? Fuel pressure?

Does it run OK once up to speed? Or is the stumble always there?

Edit: Didn't someone once say that 90% of carb problems are in the ignition?

WE need a pic of the WHOLE car.then we might be able to figer it out.

I'm not sure of the jets, float level etc as I've just started trying to troubleshoot.

It does run a lot better at highway speed but on occasion will stumble and spit if accelerating up a hill or to pass, etc.

IMO ... Needs a pump shot jet OR a longer cycle

Do you know how to adjust the accelerator pump arm on Holley carbs properly?
If not try holding the throttle wide open and adjust the accelerator pump arm SCREW so it has around .015 travel to bottom the pump lever out against the pump rubber in the pump at WOT
Lots of people mess that up real bad, which will make the pump not squirt immediately when you open the throttle even a tiny bit
Check your pump now to see if it does squirt right away when you open the throttle a tiny bit

Your power valve rating is too low, it needs to open sooner than yours. Pull the PV and check the rating, if it's a 5.5 go to a 6.5, if it's a 6.5 go to a 7.5 etc... I've pulled Holley's apart and found PV's as low as 3.5's, that's alright for a race car with a giant cam but not good for a street car.

Initial timing too low?

I haven't messed with too many Holley carbs. Always AFB/AVS and Thermoquads.

However, I will look at some Youtube how-to videos and adjust pump arm and look at the power valve and see if we can work this out so the car quits running like crap.

I agree with Dr Charles. Most likely lean in the transition port. Could be too much timing or such, but if its fuel, then the initial throttle position may be out of the working range.

A couple of ways to verify. In neutral, slowly increase throttle from idle. If it hesitates or misses, then its idle circuit. If not, then try it with load on it - that is driving it opening the throttle as slow as you can. If no hesitation, then look at pump shot.

If it misses in the tests, try repeating with richer idle mix and see if that helps.

On the Holley type designs, its very important the primary side throttle position at idle reveals .020 to .040" of transition slot below the blades. Then readust the idle mix using the screws.

....after a few months of messing with the problem when I had spare time I finally resolved the issue(for those who are interested or the resolution may help.)

It turns out the intake manifold was leaking around the #1 and #8 ports. Whoever installed gaskets on the engine before I got the car put a wrong sized gasket between the valley pan and head. The gasket had dried and broken causing the gaps allowing the air to get in. They had the correct size gasket between the intake and pan. So..... I'm not really sure why that happened.... maybe a non Mopar experienced person was the installer.

I removed the intake/valley pan, re installed and sealed it on both sides of the valley pan.... now it has clean acceleration and idles as it should so I can FINALLY drive and enjoy it now !!!

success ! feels great when a problem gets solved, especially one that is troublesome to diagnose.
glad for you it's finally solved !