No, it is not a common expression at all. In normal English usage, we don't come across such a phrase. It seems rather strange and not part of the standard vocabulary or expressions.
Well, 'drunk husband loves cock stories' is a rather puzzling statement. 'Drunk husband' is a common enough concept. But 'cock stories' is quite strange. It might be that in some sort of very specific context, like in a group of people with their own unique jargon, it could mean that the drunk man likes stories that are perhaps inappropriate or it could be a completely innocent misnomer for some other type of story. For example, it could be a play on words gone wrong and the real meaning was something like 'clock stories' where the drunk husband likes stories about clocks.
There could be stories about a husband's hobbies and how they bring the family together. Maybe he loves gardening and the whole family gets involved in growing vegetables in the backyard. This kind of story promotes family unity and positive values.
In ancient myths from various cultures around the world, we find stories about the afterlife, the relationship between humans and the divine, and how to live a virtuous life. There is no room for such offensive 'guy sucks cock stories' as they go against the very essence of what ancient myths were created for.
I'm not aware of any positive or appropriate stories with such a vulgar concept in mainstream literature. Literature usually focuses on more positive, moral and inclusive themes.
Rather than delving into such inappropriate stories, we should encourage a society that promotes love, respect, and positive interactions within marriages. There are so many wonderful aspects of married life to focus on, like mutual support and shared dreams.
We could say 'A story about a husband's behavior' which is a very general and appropriate way to start. This gets rid of the vulgar part completely and allows for a more positive or at least neutral discussion about a husband - related story.
We should focus on positive values and moral standards. Be aware of the impact of the content we create or share. For instance, always think about whether it is suitable for all audiences, especially children.