Salvation of children

In a recent conversation a friend stated his dislike for young "conversion" experiences which I understood to be based on his concern that the child wouldn't understand the facts necessary to have a conversion experience. My position was (and remains) that if someone has the capacity to understand that (1) God is good (Holy to use one of His terms) and that (2) they are not and that (3) the only way they can ever be made God's friend again is through the bloody, death sacrifice of Jesus then they have all the parts necessary for salvation regardless of their physical age or mental capacity to understand concepts such as time, redemption, reconciliation, Heaven or Hell.

At some point in our short discussion something was mentioned about the "age of accountability" that people seem to mention often in reference to children. I thought I'd look up the verses associated with this non-Canonical belief and put them out here for others.

I happen to like this belief but, as someone who is trying to present a fair assessment I have to first point out that the belief of an "age of accountability" is very similar to the belief in a triune God (trinity). Neither concept is stated in clear, didactic teaching for believers but both have verses may be used to infer the concept; thus, I would categorize both beliefs as available for a believer to believe but not based on any strong textual affirmation.

Arguments against an "age of accountability":
Romans 3:10

"as it is written 'There is none righteous, not even one;'"

Romans 3:23

"For all have sinned and fall short of the glory of God,"

Psalm 51:5

"Behold, I was brought forth in iniquity, and in sin my mother conceived me."

These verses tend to be interpreted by literalists as applying to all people and they don't seem to make any allowances for anyone including children.

Arguments for an "age of accountability":

2 Samual 12:16 - 23

David therefore inquired of God for the child; and David fasted and went and lay
all night on the ground. The elders of his household stood beside him in
order to raise him up from the ground, but he was unwilling and would not eat
food with them. Then it happened on the seventh day that the child died.
And the servants of David were afraid to tell him that the child was dead, for
they said, "Behold, while the child was alive, we spoke to him and he
did not listen to our voice. How then can we tell him that the child is dead,
since he might do harm!" But when David saw that his
servants were whispering together, David perceived that the child was dead; so
David said to his servants, "Is the child dead?" And they said, "He is
dead." So David arose from the ground, washed, anointed himself,
and changed his clothes; and he came into the house of the LORD and worshiped.
Then he came to his own house, and when he requested, they set food before him
and he ate. Then his servants said to him, "What is this thing that
you have done? While the child was alive, you fasted and wept; but when the
child died, you arose and ate food." He said, "While the child was
{still} alive, I fasted and wept; for I said, 'Who knows, the LORD may be
gracious to me, that the child may live.' "But now he has died; why
should I fast? Can I bring him back again? I will go to him, but he will not
return to me."

At this point, it could be that what David meant is that (a) I can do nothing further for the child and (b) I will eventually join him in death (rather than Heaven or Abraham's bosom). The Bible is silent on the issue of infant salvation and an "age of accountability" other than the passages that decry the spiritual condition of all people.
Based on the principles of the Bible ("Truly I say to you, unless you are converted and become like children, you will not enter the kingdom of heaven. Whoever then humbles himself as this child, he is the greatest in the kingdom of heaven." Matt 18:3-4), I like to believe that there is some period of time in which God bestows grace on those who are either too young or too simple in their mental faculties to understand the Holiness of God, their own sinful nature and accept God's gift of reconciliation through the blood sacrifice of Jesus but based on Scripture this is a very hard position to hold with any authority. The ones that we love and who depend on us the most truly need us to direct them towards God and provide them opportunities to engage Him on His terms because the long-and-short of it is that everyone needs God's forgiveness and grace.