There's also 'Sirius's Silent Sobs' which is quite moving. It focuses on a particular moment in Sirius's life when he feels most alone. The story builds up the atmosphere really well, making you feel his pain as he cries. It's a short but impactful piece of fanfiction.
One popular 'sirius black crying fanfiction' is 'The Pain in His Eyes' on FanFiction.net. It really delves deep into the emotional turmoil of Sirius. The author does a great job of showing his vulnerability and the reasons behind his tears, like his longing for a normal life outside of Azkaban and his love for his friends.
Another great one could be 'When Sirius Weeps'. This fanfiction takes a different approach. It shows Sirius crying not just from sadness but also from a sense of hope. It has some really beautiful descriptions of his emotions and how his tears are a sign of his humanity in the face of all the darkness he has endured.