Looking at the quoted verses:
Deu 5:9 You shall not bow down to them or serve them; for I the LORD your God am a jealous God, visiting the iniquity of the fathers on the children to the third and fourth generation of those who hate me,
This verse does not say the children are not innocent. Instead, the more probable meaning is that sometimes children are targeted as further incentive for people not to make God jealous. That and it might illustrate how hot God’s jealousy burns. Note: Calvinists don’t think God has emotions (impassibility).
Piper wants to use this verse mechanically with the next quoted verse to prove children are not innocent:
Eze 18:20 The soul who sins shall die. The son shall not suffer for the iniquity of the father, nor the father suffer for the iniquity of the son. The righteousness of the righteous shall be upon himself, and the wickedness of the wicked shall be upon himself.
Throughout Jeremiah God is said to target children. In Ezekiel, God is saying no longer will He do that but now He will distribute justice more evenly.
Ezekiel 18:20 seems like a reversal on God’s part. Note: Calvinists do not think God can change His mind (immutability).
In any case, the context of Ezekiel is to say that God will not kill innocent children, something that Piper denies is possible. Even if the children in Deu 5:9 were “guilty”, this hardly means all children are guilty and this hardly means that Eze 18:20 is saying that the children in Deu 5:9 were guilty.
God is Open 
Deu 5:9 You shall not bow down to them or serve them; for I the LORD your God am a jealous God, visiting the iniquity of the fathers on the children to the third and fourth generation of those who hate me,
Might this simply mean that the consequences of the father’s sins are experienced by the children. E.G. If a father commits murder and is imprisoned or executed, the children do not have a father, the mother is left alone to raise the children, etc. We have this situation today when many “fathers” do not even marry the women they have children with and often simply disappear. The children live with the consequences of his behavior. With respect to the number of generations affected, we may be getting some insight into how long such consequences last due to the social nature of those consequences. Sorry, if this is not spelled out very well, but I think this approach eliminates some of the nonsense that certain individuals create in trying to read their Calvinist doctrines into scriptures of this kind.
It could be. But it sounds to me like God is visiting the judgment through generations. In 1 Sam 15 we see an example:
1 Samuel 15:2
Thus says the Lord of hosts, I have noted what Amalek did to Israel in opposing them on the way when they came up out of Egypt.
We also see an interesting delayed judgement here:
1Ki 21:29 “Have you seen how Ahab has humbled himself before me? Because he has humbled himself before me, I will not bring the disaster in his days; but in his son’s days I will bring the disaster upon his house.”
When your belief system becomes so rigid, so inflexible and so certain of its correctness, that you cease caring about who might be listening, and undermine belief in God as a God of Love,
then you’ve made the same fundamentalist religious mistake that God ended up attacking through the Old Testament prophets.
Amos 5:21
“I hate, I reject your (correctly practiced) festivals,
Nor do I delight in your (Biblically obedient) solemn assemblies.“
See also Isaiah 1:11-16; 66:3; Amos 4:4, 5; 8:10; Jeremiah 14:12; Hosea 5:6.
Sir,
Thank you for your comment. A few issues:
1. When we start into dignum deo theology, we start encountering subjective territory. Take spanking: reasonable people may disagree on if spanking children is “good” or “evil”.
2. Verse trumping is generally a bad practice. We have plenty of incidents in which God punishes children for the crimes of their parents (the flood being a primary example). My Jeremiah link has explicit references. If you are appealing to board statements to override explicit incidents, that is not the way generalization works.
Also… In my about section, I don’t claim to represent all Open Theists. I encourage you to write your own rebuttal to Piper and I will publish it here. I don’t claim a monopoly on the ideas that can be presented on this blog.
Thanks!