Interesting Discussion This discussion touches numerous very important and often ignored issues. The "riddle" of Cornelius, Jereboam's infant son, Rachel's Children (Jer 31), and David's infant son with Bathsheba is resolved by having a biblical definition of regeneration - namely that it imparts eternal life (Eph 2:1) and precedes the exercise of faith in time (I John 5:1, John 5:24).
Once this is established, there are numerous theological ramifications.
1) The exercise of faith is TOO LATE in the ordo salutis to EVER account for the IMPARTATION of eternal life which preceded it in regeneration.
2) God's elect people whether infants, imbeciles, or lacking any explicit gospel instruction (I Cor 15:3-4) are all saved by sovereign regeneration (Tit 3:5) in precisely the same fashion (John 3:8) irrespective of their relative conditions or the amount of gospel light they have been given.
Looking more closely at Cornelius:
A) Cornelius was devout. Search the underlying Greek word out and you'll find that the men it is used in reference to are ALL regenerate men (Noah, Lot, Annanias, those in Cornelius's house).
B) Cornelius feared God. Paul's testimony is that the unregenerate man has "no fear of God." (Rom 3:18)
Cornelius was a regenerate man in Acts 10:2
Great Sermon! Peter's confession of Christ (Matt 16:16) makes absolutely certain that he is born again and thus already in possession of eternal life (I John 5:1) at the time of v16. His subsequent denial of a fundamental tenet of the gospel, the crucifixion of Christ, both before it happened (Matt 16:22) and after it had happened (Mark 16:14) stand as an ironclad proof that the gospel does NOT regenerate men. The Lord quickens whom he will without any assistance from man whatsoever (John 3:8). Belief of the gospel is a lagging indicator of a grace already imparted in sovereign regeneration, not a prerequisite to obtaining eternal life.
Perhaps Paul said it best: "But is now made MANIFEST by the appearing of our Lord and Savior Jesus Christ, who hath abolished death, and hath brought life and immortality TO LIGHT through the gospel." (II Tim 1:10) Christ gives life, the gospel gives the light of information to those who have the spiritual eyes to see the kingdom of God (John 3:3).