Unless Amy Sherman Palladino decides to rally everyone together for another reboot of "Gilmore Girls", we may never know who the father of Rory's child is, but after rewatching all of "Gilmore Girls" and "Gilmore Girls: A Year in the Life", I think I have a pretty good idea of who the dad is, and unfortunately, it's not who I always pictured Rory with (sorry, Jess).
I had a suspicion earlier on in the reboot that Rory's infamous one-night stand might be the father, but that seemed too dramatic for the show. And no matter how many times Rory and Dean seemed to reconnect, I didn't think he was the father either, since Dean finally seems happy. Instead, I believe that Logan Huntzberger is the father of Rory's mystery child.
Let me explain: I don't think Rory was desperate enough to think that she could convince Logan to stay with her if she had his child, and I seriously don't think she intended to make their last Life and Death Brigade-inspired night to end with a child inside of her. However, birth control is never 100% safe, and neither are condoms, so it's quite possible that Rory and Logan are the parents of everyone's favorite mystery child.
Aside from the fact that Logan is the only man that Rory is actually seen sleeping with in the show, there was one very important scene that convinced me that Logan is Stars Hollow's newest dad-to-be: that important scene was none other than the one where Rory went to go visit her father, Christopher, in his new fancy corporate office. Rory asks her father whether or not he thought that it was the right choice to let Lorelai raise Rory on her own, with no support from anyone else, and Christopher obviously has a hard time answering the question. However, Rory asks the question with the excuse that it's for her book, but I think that she was really asking because she wasn't sure if she should tell Logan that she's pregnant or if she should let him help raise their child.
If you recall, Christopher originally doesn't like Logan because he thinks that Logan acted just like he did when he was Logan's age, and that concern is understandable. Logan was irresponsible, hot-headed, came from a snotty family, and had no problem sleeping around. In the many years since Logan and Christopher met, not much had changed for either of them, and that's very concerning for Rory's baby. Christopher was a terrible father to both of his children, so why would Logan be any better, especially when he's engaged to another woman?
I would bet serious money on Logan being Rory's baby daddy, especially since Amy Sherman Palladino apparently told Matt Czuchry, the actor who plays Logan Huntzberger, the identity of the father! However, Czuchry refuses to name the father because he believes that is it not his place to do so. That being said, why would Czuchry be told who the father is if it isn't his character? What more proof do you need?