I played a Martell deck last night built around the "House Dayne" trait, and it worked really well. Today, when I started trying to recall the decklist, I realized that an effective version of the deck could be built using using only one copy of each of the following:

1 x Core Set
1 x Princes of the Sun (Martell Deluxe Expansion)
1 x A Song of Summer (A Time of Ravens Cycle)
1 x The Winds of Winter (A Time of Ravens Cycle)
1 x The Raven’s Song (A Time of Ravens Cycle)
1 x A Sword in the Darkness (Defenders of the North Cycle)
1 x The Wildling Horde (Defenders of the North Cycle)
1 x Return of the Others (Defenders of the North Cycle)

I don't think this is an optimal deck (for example, it doesn't include Venemous Blade, simply because that didn't fit with the theme), but it is a fun deck and an effective deck. The Starfall Advisors and Healers work to save your characters and cancel any nasty abilities or events, while the Knights of the Sun can easily become huge powerhouses (since with Starfall and Summer, each gold token on them gives them +2 STR). It's well balanced across the three challenge types, and the draw bonus from the agenda should keep your hand full. And, it wouldn't be Martell if there weren't a bunch of events that made your opponent regret he ever challenged you.

So here it is:

Summer Dayne

Plots (7)

1 x To the Spears (Princes of the Sun)
1 x A Song of Summer (A Song of Summer)
1 x Wildfire Assault (Core Set)
1 x A Time for Ravens (The Raven’s Song)
1 x Mutual Cause (Core Set)
1 x Tourney for the Hand (Core Set)
1 x Mutual Blackmail (Core Set)

Agenda (1)

1 x Kings of the Summer (A Song of Summer)

Characters (30)

3 x Carrion Bird (A Song of Summer)
3 x Starfall Bannerman (A Song of Summer)
3 x Knights of the Sun (A Song of Summer)
1 x *Ser Arthur Dayne (The Winds of Winter)
2 x *Darkstar (Princes of the Sun)
2 x House Dayne Knight (Princes of the Sun)
2 x Lord Edric's Knight (Princes of the Sun)
2 x House Dayne Skirmisher (Princes of the Sun)
2 x House Dayne Reserves (Princes of the Sun)
3 x House Dayne Squire (A Sword in the Darkness)
3 x Starfall Advisor (The Wildling Horde)
3 x Starfall Healer (Return of the Others)
1 x *The Red Viper (Princes of the Sun)

Locations (16)

2 x Dornish Fiefdoms (Princes of the Sun)
2 x Palace Fountains (Princes of the Sun)
2 x Water Gardens (Princes of the Sun)
1 x *Lord Doran’s Chambers (Princes of the Sun)
3 x Summer Sea (Princes of the Sun, Core Set)
2 x Crossroads (Core Set)
1 x *Dorne (Princes of the Sun)
2 x *Starfall (A Sword in the Darkness)

Attachments (4)

1 x *Dawn (The Raven’s Song)
3 x Black Raven (A Song of Summer)

Events (9)

2 x Red Vengeance (Princes of the Sun)
2 x Parting Blow (Princes of the Sun)
2 x The Prince’s Wrath (Princes of the Sun)
3 x Burning on the Sands (Return of the Others)

Yup... I like it! I've done something very similar. It's fun to play.

I'll throw out some fairly obvious tweaks which don't really apply to the "on the budget" subject, but you might want to consider adding a Maester of the Sun (or two) and maybe triple Darkstar. You can kneel MoS to discard him (thereby putting him into play) to save another character from being killed. Maybe Gilly for even more draw. And I've also found that the new(ish) Raven event card Ill Tidings works very well in this deck, since the Martell refugees are Maesters as well. As you say, when coupled with trusty Martell attachments and events, you've got a pretty solid deck.

Just be ready to put your brain into math overdrive when you play Targ burn..!

Good call; in my personal version of the deck, I do run Maester of the Sun (I also run x3 of several Princes of the Sun non-uniques, but only 1 Darkstar. Hmmm).

And it's funny you should mention Targ Burn, because that's exactly what I ran against this deck last night. And yeah, math overdrive.

"Let's see, your Knights of the Sun have 3 gold tokens on them, so that's +3, but Starfall is in play, so they get another +3, but I've put poisoned wine on them, so that's -2, but you played Tourney for the Hand, so that's +1, but I played Forever Burning, so that's -1, but you cancelled it with Starfall Advisor, so that's...

...do you want to just play LCR?"