During the wedding scene Liv is crying and she explains to Emma that she's been crying a lot lately. Are we to assume that Liv is already pregnant?
If Liv and Emma have been friends since childhood their menstrual cycles could be in sync, which makes for an interesting last scene in which they discover they have the exact same due date. This would mean they conceived at the same time, making Fletcher the father of Emma's child.
Liv was saying she cries all the time because she was finally letting go of holding her emotions in. She was constantly trying to be perfect, and that meant NOT crying or showing emotions, and "having it together all the time".
Also, even if their cycles were in sync, the last scene when they both revealed their pregnancies was one year later, and pregnancies generally last 8 or 9 months. If that were the case, they would have had their babies a few months before that "one year later" scene.
To answer your question, Liv's brother was the father.
...unless Emma was cheating lol