Most of 4e’s published (hardcopy) material was not Forgotten Realms and I don't think there are any specific 4e accessories for Amn. Fortunately for you, most of the 4e Living Forgotten Realms adventures are available for free online. While I don't know if there are any additional adventures based in Amn itself, as you noted there are a couple of Amnite colonies—Port Nyranzaru in Chult and Snowdown in the Moonshae Isles. Available Living Forgotten Realms adventures in the Moonshaes involving Amn and Amnian mercenaries are:
- Nature’s Wrath – Amnite pirates in the Moonshaes
- Black Gold – An Amnite agent in the Moonshaes
- Black Blood – A major encounter with Amnian mercenaries in the Moonshaes
- Black Heart – Adventure ties in with the Amnite agent from Black Gold
For more in-game historical background, there are the Forgotten Realms Campaign Setting and Player’s Guide for 3e, particularly the Shadow Thief of Amn Prestige Class in the latter.
In addition, AD&D 2e contains several Forgotten Realms accessories that directly deal with Amn, although these take place during the Time of Troubles in Faerûn before the Spellplague of 4e. Specifically,
- Lands of Intrigue – Book Two: Amn (60+ pages)
- Empires of the Sands – The first 18 pages are dedicated to Amn
- Volo’s Guide to the North – Many references to Amn are interspersed throughout
You could also use material from Baldur’s Gate 2: Shadows of Amn, the computer game and the novel, which are centered in Amn and prominently feature Spellhold.
Dragon and Dungeon magazines have some Amn-related articles. For example, "Crimmor: City of Caravans" by Ed "I am Elminster!" Greenwood in Dragon #334 (pp. 22-34) is a loquacious, detailed treatment of the "Crossroads of Amn," including a keyed map, that was nominally for 3.5e but contains almost no mechanical information. (Courtesy of @HeyICanChan. Thanks!)
There are a couple of old 4e WotC forum threads on Amn. One, entitled "Heroic Tier Adventure Ideas for Amn," is self-explanatory and the other is "Meldread's Amn," one DM's detailed version of Amn about 100 years after the Spellplague, including maps.