No. Writing NSFW (Not Safe For Work) fanfic, especially involving such characters, is inappropriate as it often goes against ethical and moral standards. It can also be disrespectful to the source material and its intended audience.
One idea could be that Peter and Quagmire start a business together. They might open a bar where all sorts of crazy things happen. For example, they could have themed nights inspired by their wildest adventures in Quahog. Another plot could be that they get lost in the woods while on a hunting trip and have to rely on each other's skills to survive. Maybe they find a mysterious cave and discover something that changes their friendship forever.
You could write a friendly adventure fanfic where Peter and Quagmire team up to solve a mystery in their neighborhood. For example, they could work together to find a lost pet or figure out who is causing strange noises at night. This would focus on their friendship and the positive aspects of their characters.
The 'Joe vs Carole' story has a lot of elements that are hard to separate fact from fiction at first glance. Factually, there were real - life events and legal issues between the two individuals. However, in the media and public perception, some details might have been exaggerated or misconstrued as fiction. It's important to look at reliable sources like court documents to really understand what's fact and what's not.
They could start by sharing a common hobby like fishing. Spending time together on the lake, they'd bond over their catches and the ones that got away. This would be a simple start to building their relationship.
Lois could be a great addition. Her relationship with Peter and her reactions to his antics with Quagmire can add a lot of drama. Also, Cleveland. His calm and collected nature contrasts with Peter and Quagmire's craziness. His interactions with them can lead to some really funny moments.