Rock Lee might be an interesting choice. He is Neji's friend and has a strong sense of loyalty. He would be very dedicated to taking care of the baby. His physical strength could also be useful in case of any danger. And his positive attitude would be great for the baby's environment.
Naruto and Neji's friendship in fanfiction often delves into their past traumas. Naruto understands Neji's pain of being in a rigid clan structure, and Neji realizes Naruto's loneliness from being an outcast as a child. This mutual understanding cements their friendship. They support each other in battles, with Naruto relying on Neji's strategic mind and Neji depending on Naruto's raw power and determination.
A common theme is his struggle with the Hyuga clan's traditions. Since the Hyuga clan has strict rules and expectations, many fanfics explore how Akito deals with them. For example, he might be trying to break free from some of the more archaic traditions while still maintaining his loyalty to the clan.
One great Hinata Hyuga depressed fanfiction is 'Shadows of the Heart'. It delves deep into Hinata's insecurities and how she copes with the pressures around her. The author does an amazing job of portraying her inner turmoil in a very relatable way.
One common theme is Hinata's growth. Fanfictions often explore how she develops as a ninja, both in terms of her physical abilities and her mental strength. Another theme is her relationships, especially her relationship with Naruto. Many fanfictions build on their relationship, showing different scenarios of how they interact and support each other.
I'm not sure specifically about extremely popular 'Neji and Ino Married' fanfictions. However, you can search on fanfiction websites like FanFiction.net or Archive of Our Own. There might be some hidden gems there. You could also join Naruto - related fan communities on platforms like Reddit or Discord and ask for recommendations. Chances are, other fans will be able to point you to some great stories.
One great Neji and Gaara fanfiction could be 'The Bond Beyond Clans'. In this story, they start off as rivals but gradually come to understand each other's pain and form an unlikely friendship. It beautifully explores their characters' depth.
There may be a vast amount of fanfiction about Neji and Sakura, but 'Hard Lemon' implies something that is not suitable for general consumption. It's better to look for fanfiction that respects the characters and the overall spirit of the Naruto franchise. This could include stories about their adventures together, or how they interact with other characters in the series.