This is my idea: Knights + Cities with low cost characters and Dondarrion with infamy.

1x Valar Morghulis (Core Set)
1x Forgotten Plans
1x City of Lies
1x City of Sin
1x City of Secrets
1x City of Spiders

1x City of Soldiers

Characters:

3x Vendor of Venoms
3x Refugee f the Citadel
3x Flea Bottom Scavenger
3x Dornish Paramour
2x House Messenger
2x Maester of Lemonwood
3x Beric Dondarrion
3x Thoros of Myr
1x Tom Sevenstrings
1x Lady Stoneheart
3x Pyromancer's Apprentice

3x Carrion Bird

Attachments:

3x Taste for Blood
3x Devious Intentions
3x Venomous Blade

Events:

3x Red Vengeance
3x Burning on the Sand
3x Blood for Blood
2x Nightmares
2x Ill Tidings
2x The Hand´s Judgement

Locations:

1x Shadowblack Lane
1x street of Sisters
1x street of steel
3x Summer Sea

Did you mean Brotherhood Agenda? Beric doesn't do anything special once you have power on your house card, and I don't think you can build a deck like this and hope to get both Beric and Devious Intentions even if you have a lot of draw mechanics.

No, I mean "Knights of the hollow hill" without brotherhood agenda. I use Infamy to keep power on characters while i use the gold and influence of Hollow Hill with cities.

Assuming you can get this to work, how do you plan to push through a win against the current popular/powerful deck types? I just don't see what you are going to be able to do to threaten a military, kneel, or power rush deck type, especally when you are going to have to run so conservative if you don't get an infamy card out first turn.

My suggestion is that you need more control, perhaps some of these cards would help

Lost Oasis

Poisoned Knife

Varys (SaS)

Ser Arys Oakheart

Out of curiosity, why play with Brotherhood if you aren't using the Brotherhood Agenda? Beric's just a 4-cost tricon with renown, you can probably find a better tricon with renown with an ability that is useful. If you don't draw a Devious Intentions or if it gets removed from play, Beric and all your Brotherhood characters lose their abilities once you get a single power on your house. It seems like you are basing the whole deck on your ability to get several Devious Intentions out and then keep them out, and you can't really count on this.

Well, Vendor of Venoms does have Infamy. But it seems rather risky to run this type of deck out of Martell rather than Lannister. I am assuming it is more based off of challenge control and the amazing Martell draw engine.