Currently the deck has 65 cards and is intended for melee. It’s a summer baratheon deck but summer is not essential to the theme. (And I’m probably going to try out a non-summer variant.) The decks itself has quite a few renown characters (like most baratheon decks but it’s not made for rushing. It takes a more defensive approach with quite a few characters that are immune to certain effects and standing effects.

Agenda
King Of summer
Plot
Mutual Blackmail
Mutual Enemies
The Power of Blood
Fury of the Stag
A Time for Ravens
A Song of Summer
An Empty Throne

Characters: 37
3 Robert Baratheon(king and stand if no shadow)
3 Renly Baratheon
1 Brienne Of Tarth
3 Knights of Flowers (latest version)
1 Axel Florent
3 Summer’s Champion
1 Margery Tyrell
1 Sallador Saan
1 Ser Axel Florent
1 Edric Storm
1 Devan seaworth
1 Davos Seaworth
3 City Watch
3 Eddard stark
3 Priestess Of Pyre
3 Royal Entourage
1 Jon Arryn
3 Carrion Bird
1 Gily
Locations: 16
3 Summer Port
3 Narrow Sea
3 Stormlands Fiefdoms
3 Aegon’s Garden
1 Street of Sisters
1 King Robert’s Chambers
1 Claw Isle
1 Dragonstone port
Events: 6
3 Lords Of the Narrow Sea
3 Distinct Mastery (might ditch those)
Attachments:6
3 Black raven
3 Bodyguards.

If you want to make a more defensive Barry deck, why not make it winter instead?

making it winter gives you access to cards like the Burning Sword and, more importantly, The Wall. You can combine the standing effects with not needing to kneel to defend to make sure you win dominance. You can also include maester aemon for further defense.

Barry winter is better for what you're trying to do. Summer is much better for rush.