Just to add my bucks worth.
I pay attention to who is coming out. If it is the pitching coach, I will give them a good 30-40 seconds to talk to their kid. I then purposely walk out to the mound and say something like "Okay guys, let's go". Pitching coaches don't argue balls and strikes. If they do (hasn't happened in years for me!) I would simply tell them to "can it coach". If they persisted, I would not hesitate to eject them. I will NOT allow an assistent coach to take pop shots at me concerning my calls. I don't care how "obvious" they are when they do it, I just don't allow it. It is not their job.
If the manager (okay, this is high school, Head Coach) comes out, and I know they have a pitching coach, he is most likely going to make a change. I get ready for that change, but I am not going out there for a bit. If he stalls for more than about 40 seconds, then I head out and simply ask once I get there "What are you going to do skip?". Usually, he is just stalling to allow his reliever to warm up some more. He usually calls him out when I get to the mound. I get a name/number and get out of there.
If the Head Coach starts to make comments about my calls/strike zone, I ask "Skip, are you out here to argue balls and strikes?". If he starts to argue them some more, I simply say "Conference is over, let's go". If he doesn't comply, he goes. I have only had this happen once in over 20 years!
In college games, I do it a bit different. If the Head Coach comes out, I head straight to the mound after he get's there. In college, the manager almost never comes out unless he is going to make a change. So, no use wasting any time. It is NOT a conference if he is changing pitchers eh?
Handling coaches who argue balls and strikes is a delicate thing. I think if you are a CONSISTENT umpire, you won't have much problems, but no matter how consistent you are, some coaches are going to be jerks some days, and you HAVE to deal with it. For the good of the game you MUST deal with it, and deal with it quickly.
I follow this:
1 - Seemingly ignore the first comment. Yes, I hear it and make a mental note of it, but I don't even give them the benefit of a look.
2 - On the second comment give them a "look". I MAKE SURE they know I heard them, and usually I have a bit of a scrowl on my face when I am looking. Believe it or not, 80% of the time, I hear nothing more from the coach after this!
3 - On the third comment. I call time (if need be), take off my mask, turn to the coach, stick my hand up with palm facing him and state in a voice that everybody in the county can hear "Coach, no more arguing balls and strikes. I have heard enough". Usually you get a bit of a chirp from them, and I follow that with "Coach, ENOUGH!!!". I put my mask back on and put the ball in play.
4 - If at any point after 3 the coach makes more comments about balls and strikes, I run him. It is VERY important that you do 3 correctly! EVERYBODY should know that you just warned the coach about arguing balls and strikes and that you will not take any more of that. If he makes another comment and you run him, nobody can say that you didn't warn him right?
The above is a VERY accepted proceedure for dealing with arguing balls and strikes.
If an assistent coach argues balls and strikes, I go straight to 3, then 4.
If I make it to step 2, and don't hear anything for a few innings, then hear another comment, I will probably repeat 2 again before going to 3. This prudent. The goal here is to shut the coach up. If 2 accomplishes that for a few innings, great, he earns "another chance" to change his evil ways!
Once I get to 3 though, that is it. NO MORE MEANS NO MORE. If you give that warning, you HAVE to follow through with step 4! You have no other option and still retain integrity! If you get to step 3, then don't eject the coach the next time he argues a pitch, your credibility is shot! You will not get any respect. I don't feel sorry for you. You must not like baseball to allow this kind of behavior to continue in a game! If you get to 3 then don't follow with 4 the next time the coach argue a call, you should quit umpiring. You are simply bad for the game! You have set a precedent, and it is not a good one!
You have made it difficult for the next umpire that has to deal with that jerk. You have made it difficult for the assignor to argue "You were warned coach" when he can come back and say "But the last guy warned me, but didn't throw me out the next time I did it!".
Again, if you are consistent with your strike zone, it doesn't matter if you call them in the dirt! If you are calling it for everybody in the dirt, the call was EVENLY called both ways, and nobody has a legitimate reason to argue any ball/strike call. They may still feel like you are a horse poop ump, but you were horse poop both ways! I have heard it time and time again from players, coaches, and fans. They just want consistency within THAT GAME! Yeah, at higher levels, it is expected that you are somewhat consistent with your peers who work games too. But, even at the college level, the coaches and players accept variations of how the strike zone it called, just as long as it is consistent!
Don't let a coach argue balls and strikes with you when you break up a mound conference. Don't argue with them. If they keep making comments, follow the above 4 steps. It will work wonderfully.