I want to dress as a wood wailer and can't seem too able to.

I really like how they look like. Is there any way they can add this in? It would be a cool side quest for each city state. Where after completion you are gifted the whole set of your city states "grunt" attire.

As I understand it, an Wood Wailer's jacket is, or rather, was, available in FFXIV, back in 1.0 in a roundabout way alas, as apart of a LWR quest (from what I recall other players mentioning the subject, the quest involved being given a damaged Wood Wailer uniform to repair, and doing so made it an equippable item that you had to turn into the NPC to complete the quest, but a number of 1.0 players held onto it and still possess it. Sadly SE has never made it available in the game in any other way, despite being so long since 1.0 (next year will be ARR's tenth anniversary).

I can't find a listing on Gamerescape for that actual item, but a close enough ARR equivelant is the Serpent Private's Jacket which is fittingly Gridanian GC gear (and so requires you to be a member of the Twin Adder in order to wear or glamour it).

Ironically, the jacket worn by the Elder Seedseer's personal guardsmen is available in the game (the misleadingly named Alpine War Jacket), which is a potential item brought back through retainer Quick Ventures (as well as a drop in Amdapor Keep NM and the Wanderer's Palace NM) - it's the same style of jacket, only the colours are different.

I'm not sure if the Knights of the Barracudda's attire from Limsa Lominsa is available, but the armour worn by the Brass Blades in Ul'dah certainly is (the Vermilion gear). So there is some of the citystates' attire available.

You can always pick through garlandtools for an NPC, and look at their equipment. From there, you can see the Wood Wailer's Jacket is indeed a 1.0 item currently unavailable, but you can go through the Shared Models list to find a suitable approximation.