I love this question because hunting for those off-the-radar pairings is my favorite part of being in a fandom. When everyone else is writing Jonerys or Braime for the thousandth time, I'm digging through AO3 tags for, like, Sansa and Gendry. Not the most common, but it's got a quiet logic to it that a lot of modern AUs explore really well. Honestly, some of the most interesting character studies come from these mismatched dynamics—stuff like Tyrion and Meera Reed, which I found in a crossover-ish fic with 'The Last of Us', of all things. The writer just threw them together in a survival scenario and it completely recontextualized both their senses of humor and trauma.
Another one I keep an eye out for is any fic that pairs a Stark with someone outside their usual orbit. Bran and Myrcella, for instance. There's a small but dedicated subset of writers who fixate on the 'what if' of that betrothal actually happening, and the political and personal fallout from it is often way more nuanced than the big battle-centric stories. It's in these quiet spaces that you see the worldbuilding of Westeros really shine, because the writer has to invent so much from a few lines of canon. You get a deeper sense of the smaller houses, the day-to-day life, the minor players. That's where the rare pairs live, and they're worth the extra filtering.