"Surely I was sinful at birth, sinful from the time my mother conceived me" (NIV).

JOEL - It is not clear at all if you compare the NIV to the King James version below:

"Behold, I was shapen in iniquity; and in sin did my mother conceive me."

The King James version refers to the fact that as a consequence of the Fall of Adam, sin is present in the world and therefore all children are conceived in sin. David's mother lived in a sinful world and therefore David was concieved in sin. He did not mean that it was a sinful act for his mother to conceive him(Heb 13:4).
In Psalms 51 David is pleading for forgiveness from God after being with Bathsheba and is explaining to God that since he was born into a sinful world, he has a propensity for commiting sins himself. Here is a clasic case where a different Bible translation gives us a completely different meaning for a scripture.

Let's compare several Bible translations for this verse:
Behold, I was shapen in iniquity; and in sin did my mother conceive me." (King James)
Surely I was sinful at birth, sinful from the time my mother conceived me". (New International Version)
I've been out of step with you for a long time, in the wrong since before I was born. (The Message)
Behold, I was brought forth in iniquity, And in sin my mother conceived me. (New Amer. Std Bible)
For I was born a sinner-- yes, from the moment my mother conceived me. (New Living Translation)
See, I was born in sin and was in sin from my very beginning. (New Life Version)
I have sinned and done wrong since the day I was born. (Contemporary English Version)
I know I've been a sinner ever since I was born. I've been a sinner ever since my mother became pregnant with me. (New International Reader's Version)
Indeed, I was born guilty, a sinner when my mother conceived me. (New Revised Standard Version)

Who but God or a prophet of God could know for sure which is the correct translation and how to interpret it?

Jesus said:
"Verily I say unto you, Except ye be converted, and become as little children, ye shall not enter into the kingdom of heaven"
If little children are so sinful then why would Jesus tell us that we must be like them to enter the kingdom of heaven?

LUKE - The Book of Mormon teaches that the disobedience of Adam and Eve in eating the forbidden fruit was necessary so that they could have children and bring joy to mankind (2 Nephi 2:23-25). In contrast, the Bible specifically declares that Adam’s transgression was a sinful act of rebellion that unleashed the power of sin and death in the human heart and throughout God’s perfect world (Genesis 3:16-19; Romans 5:12; 8:20-21). There is no Biblical support for the view that Adam and Eve could only fulfill the command to "be fruitful and multiply" (Genesis 1:28) by disobeying God’s command regarding the forbidden fruit (Genesis 2:17). The Book of Mormon teaching that these divine commands are contradictory, and that God expected Adam and Eve to figure out that in reality He wanted them to break the latter command ("of the tree of the knowledge of good and evil, thou shalt not eat of it") in order to keep the former ("be fruitful and multiply"), has no basis in logic or the Biblical text, and attributes equivocation to God.

JOEL - Adam's act could not have been a "sinful act of rebellion". He did not yet know the difference between good and evil(Gen. 3:5), and was therefore incapable of commiting any sin. His transgressing(not sin) did bring sin and death into the world as the Book of Mormon also states (2 Ne 9:6, Hel 14:16). If Adam had not ever taken the forbidden fruit he and Eve would have lived forever in the Garden(Gen. 3:3). If he and Eve were capable of having children while in the Garden and no one ever died, the Garden would have become very crowded in a very short time.

Before Adam took the fruit God told him:

"Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth." (Gen. 1:28)

How could they replenish the earth and subdue it and have dominion over the fowls of the air and fishes of the sea while stuck in the Garden of Eden? It may not spell it out in the Bible as it does in the Book of Mormon, but it is logical that it was in the plans all along for Adam to take the fruit so they could go out into the world and multiply and replenish it. God was not being deceitful. He was just allowing Adam to make the choice between a greater and a lesser commandment.