Actually, I could see a "Targaryen Rebellion" scenario working similar to the "Fall of the Lazax" from TI's Shards of the Throne expansion, with randomly dealt secret objectives for each player to either help or hinder House Targaryen.
One player plays House Targaryen and has a specific objective at the game start, and the remaining players pick a House and are each dealt a secret objective to either help the Targs win, betray the Targs, or achieve some objective solo. The default set of Houses could work, although it might be better to remove Greyjoy for Arryn, remove Tyrell and move Baratheon west, then give the Targs Dragonstone and King's Landing to start. Or possibly even further provide a map overlay that rejuggles some areas.
Targaryen always possesses the Iron Throne token and can never lose it but still shift their position on the track via bids as normal. The other two tracks change as normal too.
Having the Targ player not knowing who his friends and enemies, with randomly dealt objectives, are adds a mafia-like (the game, not the organization) layer to the regular diplomacy - is Lannister giving you support this turn because he's really your ally? Or is he just trying to butter you up?
To be honest I could even see this working as a set of houserules. , draft yourself a set of objectives and Targaryen leaders, and shift around starting areas appropriately.
-Draft a set of objectives. For the Targaryen player, the objective could always be set as the elimination of the "rebel" players (tricky, because you don't know who they are at the beginning!). Alternately, you could give them the objective of holding 9 castles to win (which probably encourages less player elimination - a good thing in my book). The other objectives should include at least an 'Eliminate House Targaryen' and a 'Allow Targaryen to Win' - add extra copies to play with the probabilities. You can get creative with the other objectives too and make some independent of the fate of the Targs, such as the classic 'Control 7 castles'
-Use the Greyjoy pieces and order tokens for the Targaryens and make a set of leader cards for them (Rhaegar, Viserys, maybe Hallane? Lot of ideas from the books). Alternately, use a renamed Grejyoy leaderset if you don't want to worry about screwing with balance (I suggest ruling that each card is +1 combat strength - Euron becomes a 5 strength card, gets renamed to Rhaegar, etc. The Targs should be strong in this scenario to make up for their lack of knowledge). I'd start them in Dragonstone and King's Landing, and give them strong forces to start with, maybe a Knight and a Footman on both, and three ships.
-Additionally, the Targaryens start with 7 power tokens, start first on the Iron Throne track, and can never lose the Iron Throne piece. Even if another faction bids higher gains the initiative, House Targaryen never surrenders the Iron Throne token and always decides the result of ties, although they still take their turn in the regular order.
-The Targs also start 2nd in Fiefdoms and 3rd on the King's Court Track. Stark starts first on Fiefdoms and gets the Valyrian Blade to start. Everyone else starts with the Influence positions as normal, though displaced to the right as necessitated by the changes.
-Make Pyke inaccessible, and count Riverrun as a small castle only. Move the Stark ship on the other side of the board (he stands in for Greyjoy to counterweight Lannister, and Arryn becomes the new northerly faction that controls the northeastern sea).
-Use the Tyrell pieces and order tokens for Arryn and make a set of leader cards for them (Jon Arryn would definitely be one, maybe a Corbray?). Alternately, just use a renamed Tyrell leaderset if you're worried about screwing with balance. Start them in the Vale for sure. Possibly another territory would be Cracklaw point? And obviously a ship as well in the sea near the Vale.
-If you're sticking with the default leadersets, you could give the Targs the Tyrell leader abilities and the Arryns the Greyjoy leader abilities, but I feel the aggressive and powerful Greyjoy leader abilities fit the Targs better.
-Baratheon's the weirdest to move on the default map. Put his Footman in Storm's End, and possibly give him the Blackwater? I'm hesitant to put him too close to Highgarden.
-Use the Dorne garrison tokens from the 5 player game on Highgarden, the Arbor, etc.
-Dorne and Lannister set up as normal.
-Then deal each player an objective card and let the Rebellion begin!
These are of course just some preliminary ideas for a Robert's Rebellion scenario. You'd probably need to playtest them a bunch to get the balance about right... the key though is to keep the scenario deliberately assymetric - the Targs have power, but not knowledge about the other players motives.