It could be Severus Snape. He has a complex relationship with Dumbledore. Maybe Snape discovers some of Dumbledore's plans that he doesn't agree with regarding Harry Potter. He then sends a Howler in a fit of anger to express his disapproval.
In the fanfiction, the Howler could be a warning from an unknown dark force. Dumbledore has been making moves to counter the rising dark magic in the wizarding world. This dark force, not wanting to be thwarted, sends a Howler as a form of intimidation. The Howler could contain veiled threats and references to past events that only Dumbledore would understand.
His mother could send the howler. In the wizarding world, mothers can be quite fierce when it comes to family reputation and she might be unhappy with Sirius's actions or friends.
Maybe it happened because he made a big mistake in a magical experiment or broke a strict school rule. That might have triggered a howler being sent to him. The possibilities are endless in fanfiction!
Perhaps another student, like Hermione, could send the Howler in a very creative twist in the fanfiction. Maybe she has found out that Draco is planning something malicious against the Gryffindors and uses the Howler as a way to threaten him into stopping.
Hermione could be the sender. If Snape has made some unfair judgment in class against Gryffindor students, Hermione, with her strong sense of justice, might send a howler to him to voice her protest.
His mother is a likely sender. She could be worried about Remus and send a Howler to remind him to take his Wolfsbane Potion regularly or to be more cautious around others. Mothers are often protective, and in the wizarding world, a Howler is a rather forceful way to get your point across.
It could be Professor Snape. He often had a contentious relationship with Harry, and if Harry did something that Snape thought was particularly wrong or against school rules in a way that affected Snape's interests, he might send a Howler.
It could be Dumbledore. He was always one to oppose Voldemort and a howler from him would be a very interesting plot point. He might use it to taunt Voldemort or to try and make him second - guess his actions.
Snape could also be a possibility. If Harry did something that Snape considered a serious offense in Potions class, like using an ingredient in the wrong way that could have caused an explosion, Snape might send a howler to scold him. However, it would probably also be filled with his usual sarcasm and dislike for Harry.