Their friends like Marshall and Lily could be important characters. Marshall might offer legal advice about the adoption process as he's a lawyer. Lily could be the one who gives them tips on taking care of a baby since she has experience with her own child.
The characteristics of such fanfiction are hard to define precisely as it goes against the norm for Barney. Usually, Barney is about friendship, learning, and fun in a kid - friendly environment. But if there is 'lemon' fanfiction, it could potentially have adult - like themes that are inappropriate for the Barney brand. This would be a very strange and unorthodox take on the character, and not something that most Barney fans would expect or want.
One popular Barney fanfiction might be those that focus on Barney's adventures in a magical land. For example, there could be a story where he discovers a hidden realm full of talking animals and has to solve puzzles to return home.
I haven't come across much 'Barney the Dinosaur Lemon Fanfiction' myself. Given that Barney is a beloved children's character, the idea of lemon (which often implies something inappropriate in fanfiction terms) fanfiction seems rather strange. However, the world of fanfiction is vast and there could be some out there, but it's not something that would be easily accessible or widely known due to the nature of the character and the potential inappropriateness of such a concept.
One possible fanfiction could be that Barney and Robin find out they're pregnant unexpectedly. Maybe they initially panic as they had not planned it so soon. But then they start to get excited about becoming parents and think about how to combine their different lifestyles. Barney might start thinking of how to be a cool dad, while Robin pictures herself as a strong, working mother.
One common theme is redemption. Barney, for example, has a complex character and in fanfiction, his journey towards becoming a better person for Robin is often explored.
Perhaps in the fanfiction, Ted and Barney are initially hesitant about adoption but then they meet a baby who really needs a home. They then decide to take the plunge. Along the way, they get support from their friends. Their friends help them decorate the nursery and give them advice on baby - care. And as the baby grows, Ted and Barney discover new aspects of themselves and their friendship.