All perfect praise be to Allah, The Lord of The Worlds, and may his peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
At the beginning, may Allah make your reward great and compensate you for this loss. We ask Him to make your child an intercessor on behalf of you and his mother on the Day of Judgment since the Prophet (PBUH) said: "If anyone has three of his children die young and resigns them to Allah, he will enter the Garden.' We said, 'Messenger of Allah, what about two?' 'And two,' he said." Mahmud ibn Labid said to Jabir, "By Allah, I think that if you had asked, 'And one?' he would have given a similar answer." He said, "By Allah, I think so too." {Ahmad}.
As far as the Diyah of your child is concerned, your neighbor isn`t liable for it because he has dug that well in his own property, not in someone else`s, not in a public street, and hasn`t permitted your child to enter his property. However, he becomes liable for paying Diyah if he had dug that well in a property other than his, or dug it in his own property and allowed people to enter it without warning them against any danger present there.
The proof of this is the Hadith where the Prophet (PBUH) said: "No blood-money will be charged if somebody dies in a well." {Agreed upon}. In other words, the owner is free from any liability. And Allah The Almighty Knows Best.