After the ship starts sinking you go down the second class stairs. At C
Deck say to the seaman "I'll take my chances." Then keep on
going down the stairs until you see Jack and Shailagh Hacker.
  Offer to get the baby from Beatrix Conkling.
Go back up the stairs and near the lifeboats(on the starbord or port
side)you will find Beatrix.Threaten to publish the letter, and
eventually Beatrix will trade the baby for the letter.
  Go back down the second class stairs say the same thing to the
seaman, then give the baby to Jack and Shailagh for the painting.

(In order for this to happen you MUST have already talked to Andrew
Conkling and done what he said.)