Innocent until conception or birth? Does Psalm 51 imply that an unborn child will have no sin?  Assuming that is true, are there any denominations that support that all unborn children have salvation?  Is there newer scripture (in the NT) that reverses this?

Psalm 51:3-5 ESV


  For I know my transgressions, and my sin is ever before me. 
  
  Against you, you only, have I sinned and done what is evil in your sight, so that you may be justified in your words and blameless in your judgment. 
  
  Behold, (K)I was brought forth in iniquity, and in sin did my mother conceive me.


Psalm 51:3-5 CEV


  I know about my sins, and I cannot forget my terrible guilt. 
  
  You are really the one I have sinned against; I have disobeyed you and have done wrong. So it is right and fair for you to correct and punish me. 
  
  I have sinned and done wrong since the day I was born.
No, Psalm 51:5 does not claim that an unborn child is sinless, quite the opposite, it says (in every translation I checked except the CEV) that they were either "conceived in sin" or "sinful since conception" which I would take to be equivalent in any case.

We are tainted by Adam's curse at conception; at no point are we without sin until we are washed of it by the blood of Christ. Therefore unborn children are as much destined to hell as any unrepentant sinner outside of the womb.

That said, there is the doctrine of the "age of accountability" that many Christians hold to, which while not strictly part of this question may be relevant to the overall answer.