Well, perhaps the baby is a key to closing a major portal to the underworld. Dean discovers this and has to raise the baby while also preparing it for this great task. Along the way, he gets help from Sam and other friends. They face various challenges from demons who want to stop the baby from fulfilling its destiny.
In some fanfictions, Dean might raise angels with a special purpose. Like he raises a group of angels to help him save Sam who has been trapped in a different dimension or something equally dire. The angels have their own motives and secrets, and as they work with Dean, all these secrets start to unfold, leading to a complex and engaging story.
Maybe an angelic or demonic entity implants something in Dean that causes the pregnancy. Dean might initially be in denial and try to hide it from Sam. As the pregnancy progresses, he starts to experience strange powers or sensations. This could lead to a journey where they discover that the unborn entity is a key to saving the world from a great evil.
One plot idea could be that Dean discovers he's pregnant and is extremely conflicted. He's worried about how John will react, as they have a complex relationship. Maybe at first John is shocked and struggles to accept it, but then realizes he has to be there for Dean. Another idea is that an enemy finds out about Dean's condition and tries to use it against them.
Maybe Dean gets cursed by a witch. The tail could be a side - effect of the curse that slowly changes him. He has to find a way to break the curse while still hunting monsters, and Sam has to deal with his brother's new 'accessory' and the problems it causes during their hunts.
A unique plot could be that their marriage gives them new powers. Since they are so closely bonded now as husbands, they can combine their powers in ways they couldn't before. For example, when facing a powerful demon, their united power makes them invincible.
One idea could be that the baby has some unique powers that are different from what was expected in the original Twilight story. Maybe the baby can communicate telepathically with all vampires and werewolves, not just Edward, which causes some chaos as different factions try to use this to their advantage.
One interesting storyline could be the baby sister having special powers that she has to learn to control. Maybe she can communicate with spirits in a unique way, different from Sam and Dean, which adds a new dynamic to their hunting adventures.
Dean would become more protective. His tough - guy exterior would soften as he takes care of the baby. He'd be more cautious in his hunts, not wanting to leave the baby unprotected.
One great fanfiction with this concept is 'Baby Dean's Adventures'. It has a really cute take on how the other characters deal with a baby Dean. They struggle at first but then it becomes a heartwarming story of protection and family.
Another fanfiction idea could be that Dean is driving and he picks up a hitchhiker who turns out to be a supernatural being in disguise. At first, he doesn't suspect anything, but as they start chatting, he notices some strange things about the person. This could lead to an exciting adventure as Dean tries to figure out what the being is and how to deal with it while still on the road.