Oberyn Martell - I've love to play him against Loras Tyrell in come capacity (or instead play Loras against him), possibly after Renly's death and during the time he and Ellaria come to court. I would also love to play Cersei against him in the same setting, and I'm dying to find a Daemon Sand to play Oberyn against in any incarnation of their relationship.
Arya Stark - Another of my favorite characters, I'd love to play her in any part of her storyline or rewrite her into something more AU against a ton of characters; preferably against Gendry (I'd kill for any sort of line with him), The Hound (a buddy cop show in the riverlands?), Cersei (what if Arya never got out of kings landing?), Podrick Payne (I love his incarnation in the show, and if he'd caught her after Brienne's fight with the Hound I could imagine a fun story with the two of them), Beric/Thoros/The Brotherhood (a female outlaw like Wenda the White Fawn), etc. Aging her up and playing with pbs is always an option as well, and all of the above pairings could be played out as both gen and romantic.
Jon Snow - is a character I would love to play a character against, and for the right Jon Snow I would play anyone from Ygritte to Grenn to Daenerys to Alys Karstark. AU is totally welcome obviously, and drama at the Wall with wildlings and white walkers would be a super bonus. If you're partial to the fan theories as I am, something to do with that revelation could be great fun to explore.
Rhaegar Targaryen - I would love to play him against Jon Connington in the years that Jon served as Hand to Rhaegar's ailing father, and maybe work in portions of the Elia and Lyanna storylines as well, and explore a lot of the dragon price's mysterious past. Again, I'd love to cook up AU versions of Rhaegar's story, but something about exploring the canon of that period is particularly appealing, although playing with his and Connington's relationship is also welcome.
And if you still love Game of Thrones and nothing above strikes you, I'm definitely willing to negotiate writing a couple that you like from the series along with one of mine (ie, I'd love to write Petyr to your Sansa, if Arya and Gendry joined them somehow in the Vale). You can always find me though this journal if you'd like to plot!