I came with some ideas where at least one new unique military unit could be trained by the Aztecs, Haudenosaunee, Incas and the Indians. The reason for giving them these new units is because they can help with fixing some problems that these civilisations have.
Aztecs
(1) Shorn One: “Tough imperial shock infantry. Can be used to divert enemy fire to them. Good against ranged infantry and artillery.” (In-game description).
The Shorn One will be available from the [Nobles Hut] in the Fortress Age. They will act as a combination between the [Coyote Runner] and the Haudenosaunee [Mantlet], where they will have a similar speed to the Coyote Runner but have a high damage resistance to ranged attacks and many hit points. They will occupy 2 population slots and can also support when sieging to a certain extent.
The Shorn Ones (Shorn meaning “Shaved”) were distinguishable warriors in the Aztec society. In appearance their heads were almost completely shaved apart from a long braid over the left ear, but according to a site known as the “The Last Diadoch” (The Last Diadoch) it points out that other sources state that the Shorn Ones had a mohawk-like hairstyle. Other pronounced features was that they had painted faces, where half of their faces were painted blue while the other side was either half red or yellow in colour. In addition the Shorn Ones were also recognised by their yellow “tlahuiztli”, which was a decorated military war suit. They were apparently the imperial shock troopers of the Aztec army and they took on special tasks as well as battlefield assistance roles when needed.
Haudenosaunee
(2) Demolitionist: “Siege unit that throws explosive spears. Good against infantry and buildings.” (In-game description).
Available in the Fortress Age together with the [Ram] and the [Mantlet], the Demolitionist unit will cover for the biggest weakness that the Haudenosaunee has in the Fortress Age, which is the lack of any ranged siege capabilities until the Industrial Age and afterwards. They will behave like a weaker [Falconet] and have a range of 24. They will occupy 3 population slots, but this can be mitigated with the [Siege Discipline] card which decreases it to 2.
Incas
(3) Kumana Prowl Runner: “Fast moving spear thrower that can go into stealth. Useful against cavalry and shock infantry.” (In-game description).
Unlike both the [Chimu Runner] unit and the [Jungle Bowman] unit who can only go into stealth mode after sending the “Cloud Warriors” card, The Kumana Prowl Runner will have the ability to go into stealth by default. They will be available in the Fortress Age and fulfill the same role as the Aztec [Eagle Runner Knight].
You might come with the argument: “But doesn’t the Incas have Bolas Warriors which they can use to counter cavalry?” Yes they do but they function more like a [Musketeer] with ranged multipliers against cavalry, just like the Swedish [Carolean], than substituting the role of a [Dragoon]. By adding the Kumana Prowl Runner to the Incan army not only will they be able ambush enemy players without the need of the “Cloud Warriors” card but they can also perform hit and run tactics as well.
According to Wikipedia the Incas did use spear throwers for warfare but it was later adopted. The weapon was apparently mainly used for guerrilla tactics to attack the Peruvian cavalry. Kumana means “Spear Thrower” in Quechua.
Indians
(4) Mysore Rocketeer: “Indian siege trooper that fires rockets. Good against infantry and buildings.” (In-game description).
The Mysore Rocketeer can be available in the Fortress Age and be trained from the [Castle] and the [Agra Fort]. They will be both a cheaper and a more population efficient alternative to the [Siege Elephant]. Their siege range can be the same as the Incan [Huaraca] which is 24.
According to a book known as “Rockets and Missiles: The LIfe Story of a Technology” (https://books.google.se/books?id=k8CxJeFzCdQC&pg=PA14&redir_esc=y#v=onepage&q&f=false) which is cited on Wikipedia, The Mysorean rocket was an Indian military weapon which was effectively used against the British East India Company during the 1780s and 1790s. These weapons were also the first iron-cased rockets successfully deployed for military use. And they served as inspiration for the Congreve rocket weapon used by the British which is available to them as a unit in the game and to the United States.