Just to clarify. When I mentioned the necessity of establishing paternity, I wasn't suggesting your boyfriend has any question about whether he's the father. It's a legal process. Many states don't establish legal paternity for unwed couples by just allowing the mother to list someone on the birth certificate. Either the father has to sign something acknowledging paternity, or a court decides. Since your boyfriend isn't going to be present at the birth, he'll probably have to sign and notarize a document where he's deployed and send it back to the states for you to file and establish legal paternity.
You need to find out what your particular state requires. For example, in NY, this is how they do it: https://www.childsupport.ny.gov/aop_howto.html. Just google "acknowledging paternity" and your state's name and something should pop up.
Tricare isn't going to let you add someone as a single Soldier's dependent without establishing legal paternity. A POA allowing you to add a dependent to Tricare doesn't establish paternity. Make sense?
Here's another form from an Army ID Card office telling you what a single male Soldier needs to add a child as a dependent in DEERS. http://www.drum.army.mil/hr/Documents/Documents%20Required%20for%20an%20ID%20Card.pdf