A story of love can also be called a love narrative. It emphasizes the aspect of it being a narrative that revolves around love. For example, many classic novels are love narratives where the plot is centered on the relationship between two characters in love.
Life account. A life account can also be used to refer to a person's life story. It gives a description of the events, experiences, and development throughout one's life.
Business achievement chronicle.
No, it's not a very common phrase. Usually, we hear more about settings for love stories like 'a romantic beach' or 'a cozy restaurant' rather than 'a shelter for love story'.