I pair Eowyn with Three Hunters and Smeagol for a deck like this:

Ring-bearer and Ring
Gimli, Bearer of Grudges
The One Ring, The Ring of Rings

Fellowship (33)
Legolas, Fearless Marksman (SF) (wounding)
Eowyn, Lady of Ithilien (SF) (wounding)
Smeagol, Always Helps (SF) (exerting)
Aragorn, King in Exile (healing for Legolas)
Aragorn, Guide and Protector (wounding)
Leowyn (healing for Eowyn)
Brego (exerting and healing)
Aragorn’s Bow x2 (wounding)
Ranger’s Sword (strength)
Knife of the Galadhrim (wounding and strength)
Ring of Guile (extra resistance for Gimli, and event recursion)
Gimli’s Battle Axe, Trusted Weapon (does a variety of things, including archery)
Bow of the Galadhrim (wounding)
Preparations x2 (wounding)
Till Durin Wakes Again x2 (healing for Gimli)
The Splendor of Their Banners (wounding)
Don’t Look at Them x2 (wounding)
Fortress Never Fallen (condition removal)
Slaked Thirsts x4 (exerting)
Quick As May Be x4 (wounding)
Swordsman of the Northern Kingdom x3 (strength for Aragorn)

Okay, so the basic idea is to wound.

Preparations can constantly re-stack Slaked Thirsts, and Till Durin Wakes Again ensures that Gimli has enough vitality left to use the ability.

Some key sites are:
Dammed Gate Stream (grabs Don’t Look at Them)
Stables (grabs Brego)
The Prancing Pony (grabs Aragorn)

Let me know if you like it.