@MassRiflemen Great idea
I have never done any serious war with riflemen and this game could be a nice opportunity.
This is my general playstyle for Redcoat Rush. Although I play No-tech-trading, I'm sure the general paradigm holds in a tech trading game. I will however outline two early game niche strats first:
Niche Starting Situation One: Elizabeth starts with mining. If enemy capitol is within 15 tiles, axe rush them on two cities; if not, great, then chop two settlers to zone them out of the good land between you and them (any land wit flood plains/gold/silver/gems/bronze/ivory).
Niche Starting Situation Two: If your neighbor is the second player to get a religion, they will build the temple of artemis (ToA). If this happens, karate chop the oracle and get horsebacking riding and chop stables and whip HA's (if you have horses) or math (and then rush construction for catapults+axes/spears). The great prophet that comes out of the oracle is used to build a shrine in the enemy holy city, which is the main reason we're getting the oracle, for the GP. Without the oracle, the captured ToA will pop a merchant before you can get a Great Prophet, nullifying the resources you put towards capturing the holy sity.
While you move out to attack, have one city build, chop and whip the great lighthouse. ToA+GL = gg. This paragraph is a niche situation however, so don't plan on this. Also, don't convert to that religion unless it's safe. With the ToA, GL and shrine city, you win. Also, if you fail to get the GL, the fail gold it good enough to at least try.
However, assuming that above situations didn't happen (which again, are niche situations) Elizabeth does very well with early monarchy. So now for the general playstyle:
1. I will always karate chop the oracle without marble to get monarchy. With lighthouses and a colossus followup, you can tech to engineering very fast in 5-6 cities and breakout with trebs, pikes and maces before 500 AD. This land grab is needed to fuel your redcoat drafts later. Only play a coastal start with 2+ seafood resources and a flat plains forest (this let's you get a work boat in 15 turns). By karate choping the oracle, you also deny the AI's the oracle which they will use to get metal casting, reserving the colossus for you. Hence the main reason to play the oracle to to secure the colossus. However going straight to the colossus that early is a misplay, so we take monarchy with the oracle.
2. On your colossus coastal economy and interior cottage economy, beeline civil service, then engineering. In no tech trading games you have maces, trebs and pikes before 500 AD on Immortal with Elizabeth. Thus I assume you can do this even earlier with tech trading enabled. Keep a small city size (5 or 6 cities) while stacking happy axes and spears and catapults to deter AI aggression. Since your city sizes often hit 14-16 during this build up (you should have monarchy). Whip forges, courthouses and marketplaces (and aqueducts) with excess up happy population. Make sure to trade for +happy resources for the forges and marketplaces. This let's you grow bigger cities.
3. Do not stack more happy units that you have coastal or cottage tiles. Build research or wealth once your commerce tiles are maximized. Once you have engineering, kill the the nearest AI with stone and build the Notre Dame, you will need the +2 happiness later to offset redcoat crafting. Keep killing with your mace/pike/treb breakout until you have 15+ cities. Do not lose your maces, use crossbows for stack portection. Upgrading these CR maces to redcoats is essential later on. Raze cities on the borders of other AI's to maintain a strong cultural boundary. Remember to karate chop the forbidden palace in the captured region.
4. Chop forges, courthouses and marketplaces in the captured cities. If you captured marble instead of stone, play the Parthenon and Great Library. If you already had marble, you should already have these. Make sure the oracle, colossus and Parthenon are all in different cities to avoid polluting your GP pool, while reserving the Great Library. for the highest food city.
5. We're now going into the pre-redcoat turtle phase. Delay economics and build walls and castles in your border cities. 6 Longbows per city with two mobile forces of 5 catapults and 10 formation promoted macemen on either wing of your empire can defend any assault. The longbows and castles will keep your maces safe from counter attacks between turns. An explorer with medic upgrades should also be present. You want to keep a low power score during this era to bait wars and farm great generals. Also when you get Dowed, it makes those AI's take diplo hits with other civs.
6. Once you have the castles and the above recommended defenses, go pacifism and milk great scientists. Double bulb education and whip unis, lib nationalism and then research gunpowder. Build the Taj Majal. Switch to nationalism and draft a musket from each city. Elizabeth's philo trait + national epic + GL + Parthenon + pacifism allows you to get 7-8 scientists very fast. Use the first two scientists for acamies (maybe a third as well), then save two for education. The remaining scientists are saved for chemistry, scientific method and biology.
Build theaters and colosseums between each musket draft unhappiness reset. Theaters and colosseums are a must with the redcoat beeline, since we will be triple drafting later in the game.
7. When the Taj Mahal finishes, go into organized religion and whip stock exchanges two turns before the end of the gold age and let hammer overflow go into grocers. You should also be teching rfiling during the Taj Majal Golden age (also consider using spies to steal guilds and banking). Also save a great person for a second gold age to follow up (great artist or the second great prophet). You want two back to back gold ages during this era. Stop all research after rifling, since you 're going to upgrade all CR maces and muskets to redcoats. Steal theology from someone during this.
8. If you have a Great Engineer, save it and follow up with democracy to get the Statue of Liberty. Mercantilism + Statue of Liberty + Representation allows you to continue research on a 0% slider while you're running a 40%-60% culture slider to offset triple/quadruple draft unhappiness. Kill the weak players while slow teching to communism on a 0% research slider.
9. If you don't have a Great Engineer, tech to steel. You have to end the game with cannons. Kill the strongest player first. Run a 100% culture slider if you must to draft 6 times from each city. Whip spies and send them ahead to start city revolts so your redcoats have no resistance. Make sure cannons fire into the machine gun nests (the strongest ai's will often tech to machine guns during this, do not use your cannons on any city that doesn't have machine guns). After 5-6 drafts, go theocracy and vassalage and promote collateral damage on your cannons and formation on your rifles (the strong enemies tends to spam Calvary, so formation redcoats are a must).
10. Don't be afraid of infantry or artillery or machines. Assuming you beelined redcoats, the enemy will only have a handful of infantry or artillery (or machines guns) if they managed to get assembly line. Highly Promoted Redcoats + cannons delete minor infantry pockets. Also the AI's are flat out ******ed. They will start building factories in their cities when they get assembly line no matter how much pressure they're under, meaning you have 10-15 turns to kill them without them making new units.
11. If the game is somehow going on. Save great scientists to bulb computers and beeline mech infantry after flight.
Final Note: Don't be afraid of grenadiers. Pinch promoted redcoats slaughter grenadiers 1v1. Also nine out of ten times the strongest AI has the mids. Switch to police state for a while when you take the mids to double cannon. production.
The strength of the redcoat is its longevity. It can easily punch up against early assembly line civs, and is immune to Calvary and grenadier spam from pre assembly line civs.
to any tile that already produces at least 2
generation and a +100% 
bonus to Universities.
generated over a standard bank. Banks are rarely build buildings as they are somewhat expensive (200
.
.
-tile with capital.
? As long as you have some cities that are able to build boats you are fine.
) and, fortunately enough, we get wet rice and what is now BFC copper.
