The point in attacking a city with Marines in a coast is to invade quickly and decisively. With the right kinds of troops, you can take as many are three, four, five, or even all the enemy civs cities in one turn using Marines to break the coastal towns as an entry point. This is only possible because you can field in Marines.
It is only superficially true that you can't match an AI's unit production based on proximity. Based on inherent level based advantages, yes, but by the time you research Advanced Flight, Proximity should be a thing of the past. Using Transports to ferry defensive Infantry is usually inefficient and inflexible. You will never be able to match home production using this tactic. Much better is to load 3 Transports with Marines supported by Bombers for the initial softening of the land target and followed by generous helpings of Artillery. 6 to 8 Transports worth of Artillery using 36 to 48 Artillery is modest, but then again, you are heading back for more, so more Transports may be redundant.
You use Airports to transfer mechanized troops to the scene of the action. For Infantry, Helicopters are much, much more efficient and flexible in terms of unit transport. If you're expecting heavy air cover, investing in Fighters on Carriers to defend the airspace immediately around the landing city may be appropriate and entirely worth the investment. Even if you don't, the tactic will work anyway.
You can use as many as 10 to 15 Helicopters to ferry troops, but in general, I find that 9 will suffice at the Monarch level, provided you take a maximum of three cities on landing, and plan ahead. You can take two only, or even just one, if you feel the counterattack is going to be especially vicious. Nine Helis will allow you to transfer 27 Infantry to your newly acquired city as a Rebase action, which I believe does not provoke air superiority attacks. If you wake them, they will be ready to move within the turn. Next turn, Rebase the Helis back to their home cities. On the third turn, you can ferry another 27 Infantry to whichever city or cities you may be holding at the time. Your Airport will typically complete at this stage, allowing you to also simultaneously transport as many Tanks as you have Airports in your home civ.
If you prepare 81 Infantry for use in defending your newfound territory, your 9 Helis can Rebase and distribute them in any city you capture within 5 turns, regardless of territory control and state of Rail and Pillage. Provided that you're within 2 transport hops away from your mainland, 4 Transports can transfer 12 of any unit every 2 turns to your landing city. Six can actually deliver 24 in the first 2 turns and 8 can deliver 12 every turn. This cost, however, quickly escalates with distance, and you may end up with ending up to 20 transports or more apart from the Transports you will need to land your Marines. Of course, your selection of landing cities will tend to be limited because of this, and the Transports are always subject to Bombers, Submarines, Battleships, and what not. And pillaging can hurt transport, and you may not need most of these once you get an Airport online. A collection of 9 Helis can transfer an average of 16.2 units per turn anywhere, in the first 5 turns.
Sixteen Helis can deliver 48 Infantry at a bunch and an average of 24 per turn on any particular landing spot you may so choose, and in any particular city you choose to invade after that. In addition, they can land the same number of Infantry anywhere within Paradrop range of their base city, allowing you instant threats to all key resources so long as you have air superiority.
In general, I find that 2 Helis per "core" city is easy to queue (more cities can build Helis vs. Transports) and more than outstrips that city's production within 10 turns of initiating transfers. You are quite apt to find yourself lacking troops at home unless all your core cities are capable of building 1 Infantry every single turn. Even so, you will then instantly transfer that new Infantry into your enemy's territory with no loss of movement and matching his production turn for turn. Together with Airlifts, Helis can completely drain your core civ production by means of transferring power.
In such a situation, even with tech advantage to the opposing civ, once the Airport on the landing city is built, just having the appropriate Gov and the first turn in a war can build a decisive edge for you.
In such a situation, capturing the first (few?) landing city(ies) quickly and efficiently reduces War Weariness significantly. If these are core and key cities, your AI opponent may not recover from the blow. After all, having to kill 48 Infantry + 50+ Artillery + 12+ Surviving Marines only two turns before having to kill another 48 Infantry and an imminent Airport is no mean feat. You should be able to quickly assess whether the enemy is capable of this, based on spy reports. Even with a technically stronger enemy army, capturing and holding onto the AI civ's 5 core cities is often decisive.
Just to illustrate the point, I find that 200 or so Infantry (plus various other units) on Communist on a moderately sized civ on a standard map tends to already strain the unit support. 16 Helis can transport 144 of these units in 5 turns. On the 3rd or fourth turn, you should be able to finish an Airport and manage at least one series of Airlifts of Tanks by the 5th turn. If you have a modest 16 Airport cities, that's 160 units, plus the 48 Artillery and the 12+ surviving Marines from the assault. Of course, the Transports shouldn't be resting their bums, either. So in 5 turns you should be able to land 220 land units on enemy territory using 11 Transports and 16 Helicopters and Airports.
On every succeeding turn, you can ferry an average of 24 Infantry and 16 Mechanized Units. Assuming the Transports need 4 turns to make the crossing, your 11 Transports will arrive with 66 more Artillery within 7-8 turns of your initial assault.
All this is possible only because you can capture the initial city on a coastal assault (and defend using that city's defense bonuses).
