A question to the umpires here on how to approach when they have the count wrong (for the purposes of this, assume they definitely have it wrong).
Have a good scorer. Simple as that. If both books agree it the count is different that makes it all easy.
If you come out and say 'my book has the count as 3-1 not 2-2' that should be enough to get any reasonable plate umpire to go through verifying the count. And as a coach you should insist they do if they do not - it is not unreasonable or hard for the PU to review the count in his mind, ask his partner for their count and check scorebooks.